bluuebunny/crossref_metadata_2025 huggingface dataset:
Societal Drivers of Food and Water Systems 1
Authors: Thompson Michael , Beck M. Bruce , Gyawali Dipak
Published: August 2018

Food chains interact with the vast, complex, and tangled webs of material flows —nitrogen, phosphorus, carbon, water, energy—circling the globe. Cities and households are where those material flows interact with the greatest intensity. At every point within these webs and chains, technologies enable them to function: from bullock-drawn ploughs, to mobile phones, to container ships, to wastewater treatment plants. Drawing on the theory of plural rationality, we show how the production and consumption of food and water in households and societies can be understood as occurring according to four institutionally induced styles: four basic ways of understanding the world and acting within it; four ways of living with one another and with nature. That there are four is due to the theory of plural rationality at the core of this chapter.
Conversation and Civility
Authors: Denis Delphine
Published: August 2018

In the wake of Italian handbooks of good manners, France forged the figure of the honnête homme from 1630 onward. If his merits were evident in conversation, it was thanks to conversation itself that he was able to acquire them. A new form of sociability flourished, one in which women played a decisive role. A host of terms concurrently attempted to define gentle and refined manners, among others civilité (civility), politesse (courtesy), urbanité (urbane elegance), and galanterie (gallantry). Trained in the school of the world, the galant homme should not be confused with the honnête homme, whose ideal, with a solid moral basis, was reshaped by the late seventeenth century. The air galant converted the social qualities of refined society into aesthetic values, thus giving birth to a new form of modern literature, although not without quite a few objections. In its social dimension as well as in its artistic achievements, galanterie was a genuine cultural phenomenon. As such, it was and remained identified for a long time as a key feature of the French nation.
Consumer Behavior in Emerging Markets
Authors: Castaño Raquel , Flores David
Published: August 2018

Emerging markets are substantially different from markets in high-income, industrialized societies. While many aspects of consumer behavior are the result of inherent psychological processes and are, thus, generalizable across countries and cultures, the specific contextual characteristics of emerging markets can significantly influence other aspects of consumer behavior. In this chapter, we explore the behavior of emerging market consumers. This chapter reviews the existing literature and proposes an initial framework delineating the main differences between emerging markets and developed markets consumers that describe how consumers in these societies recognize a need for, select, evaluate, buy, and use products. The chapter discusses the issues and contributions of the research on emerging consumers and presents implications of extant research for international managers. Finally, the chapter elaborates on an agenda for future research in this area.
Global Production Networks, Territoriality, and Political Authority
Authors: Kobrin Stephen J.
Published: August 2018

This chapter argues that structural changes in the global economy resulting from the increasing importance of global production networks (GPNs) raise complex questions about the limits of national authority and the ability to exert control over economic actors based on territorial sovereignty. In a networked mode of organization of the world economy, the nodes exist simultaneously as local and global geographies and each node’s value is dependent on its integration into the global network. As a result, the ability of any given state to exert control over a given node or the network as a whole is limited. That conflicts directly with increased demands by nationalists for local control and the domestication of production. The chapter concludes that unraveling production networks is not economically practical and that conflict with nationalists will continue into the future.
Innovation in Emerging Markets
Authors: Yip George S. , Prashantham Shameen
Published: August 2018

Multinational companies (MNCs) have traditionally conducted R&D and other innovation activities in developed countries. At the same time, most local companies in emerging markets (EMs) have traditionally imitated and adapted rather than innovated. But recent years have seen a new phenomenon of MNCs conducting R&D activities in emerging markets, and EM companies becoming significant innovators. This chapter examines the reasons for this change, especially the increases in EMs of science and technology capability, per capita incomes, customer sophistication, unique local needs, and market size. The chapter examines the innovation activities of both local and foreign companies, focusing on the two most dynamic EMs, China and India, as well as briefly reviewing other major EMs such as Brazil, Russia, Turkey, and South Africa. It concludes that innovation in EMs for both home and foreign markets is now an established and growing factor in international business.
The Economic and Sociological Approaches to Research on Business Groups in Emerging Markets
Authors: Chung Chi‐Nien , Luo Rose Xiaowei
Published: August 2018

Business groups are an organizational form prevalent in almost all emerging economies. Business groups often play a central role in the economies in which they operate by contributing high percentages of national GDP and hiring many employees. While previous reviews focus on various subjects of business groups, this chapter discusses and summarizes the literature according to four theoretical perspectives rooted in economics and sociology: the internal market view, the resource bundle perspective, the network perspective, and the institutional logic perspective. For each perspective, the chapter first summarizes the major constructs and reasoning, and then reviews key studies for each. In conclusion, this chapter calls for future research that combines these perspectives and examines the continued evolution (including the decline) of business groups.
Local Firms Within Global Value Chains
Authors: Prashantham Shameen , Yip George S.
Published: August 2018

The focus of this chapter is on local firms in emerging markets as participants in global value chains (GVCs), and how some of them make the transition from local assembler to value chain. The purpose of this chapter is not to provide a comprehensive literature review; rather, the authors discuss key GVC concepts that are relevant to their focus. The chapter begins with an overview of the GVC notion highlighting the issues of governance and upgrading. Next, it briefly reviews the following key drivers of GVCs in emerging markets: level of economic development, maturity of institutions, science and technology level, and company management capabilities. The authors then highlight the rise of EM firms within GVCs in three phases: (1) local assemblers, (2) component manufacturers, and (3) value-adding innovators and partners. The chapter closes with a discussion on the implications for international theory and future research, noting the rise of anti-globalization sentiments and the imperative for innovation within GVCs.
Investments by Emerging-Market Multinationals in Other Emerging Markets
Authors: Li Jing , Shapiro Daniel
Published: August 2018

This chapter reviews the literature on foreign direct investments among emerging economies (E-E FDI), focusing on the motivations behind E-E FDI, country-specific advantages and firm-specific advantages associated with emerging-economy multinational enterprises (EMNEs), and spillover effects of E-E FDI on host-country economic and institutional development. We identify the following topics as posing important questions for future research: EMNEs’ ability to leverage home-government resources and diplomatic connections to promote investment in other emerging economies; nonmarket strategies of EMNEs in emerging economies; ownership and corporate governance affecting investment strategy and performance of EMNEs; E-E FDI contributions to sustainable development in host countries. Future studies should also consider potential heterogeneity among EMNEs by integrating insights from institutional theory, network theory, political science, corporate governance, corporate social responsibility, and sustainable-development research.
International Business and Emerging Markets in Historical Perspective
Authors: Jones Geoffrey
Published: August 2018

This chapter provides a long-run historical perspective on international business in emerging markets. It focuses on the role of Western MNEs, and examines their strategies and the management challenges they faced. In the first era of globalization from the 19th century to the 1920s, MNEs sought access to natural resources, and benefitted from exclusive contracts. Innovation was focused on overcoming logistical challenges. During the Great Reversal during the middle decades of the 20th century, the main challenges faced by MNEs were political. Mounting hostility led many firms to divest, and to invest elsewhere. In the contemporary global economy, political risks declined, but corporate strategies needed to carefully manage relations with the government. Emerging markets were increasingly seen as indispensable by MNEs. They were both a place to locate activities in the lower end of global value chains and a growing market.
Management in Southeast Asia
Authors: Witt Michael A.
Published: August 2018

This chapter provides an overview of business and management in Southeast Asia. Drawing on the business systems (varieties of capitalism) literature, it lays out the institutional features of business in the region: Singapore as an exponent of advanced city economies and the remainder of the region as emerging Southeast Asian markets. The chapter identifies key historical themes and material forces that have led to the emergence of these ways of organizing economies in the region and discusses their key characteristics. The chapter further discusses typical strategies by foreign direct investors coming into the region as well as the state of multinational enterprises emerging from the region.
Comparative Corporate Governance in Emerging Markets
Authors: Aguilera Ruth V. , Haxhi Ilir
Published: August 2018

This chapter provides an overview of corporate governance (CG) in emerging markets (EMs). Focusing mainly on the BRIC countries (Brazil, Russia, India, and China), the chapter adopts a systematic cross-national comparative approach. It begins by highlighting the importance of better understanding CG in EMs, and identifies some of the key challenges these countries face as they seek to enhance their CG. The chapter goes on to review managerial research conducted after the year 2000 on CG in emerging markets in the following four categories: ownership, boards of directors, top management teams (TMTs), and CG practices and reform. The chapter discusses the main research questions and findings from this collective body of work. It is noteworthy how “siloed” this research has been in terms of drawing few cross-national comparisons. The third section offers an overview of the main CG features of each of the BRIC countries relative to one another, taking on the OECD Guidelines of CG as its benchmark framework. To do so, the chapter first addresses core governance areas related to the overall model of CG, ownership types and ownership rights, information disclosure and reporting, and stakeholder management and corporate social responsibility. The chapter concludes by highlighting common themes for CG in emerging markets and suggesting fruitful areas for future research.
Folklore and Folklife of American Family and Friends
Authors: Neile Caren
Published: August 2018

The folklore of family and friends is a primary social frame of traditional knowledge, promoting distinctive values, attitudes, beliefs, and behaviors. Their associated narratives share certain characteristics. They have long been mined by folklorists as popular forms of personal experience narrative, and their transmission is somewhat gender dependent. Unlike friendship narrative, however, family narrative is widely studied in its own right. This chapter argues for a deeper study of friendship narrative, given (1) its role as a performative utterance, reflecting agency that helps form and maintain the group; (2) its horizontal, egalitarian mode of transmission; (3) the effect of the relative ephemerality of friendships; and (4) the role of gossip. The tension between tradition and innovation in American society and the growing importance of friendship groups in the culture, particularly through social media, make friendship narrative an increasingly compelling area of folklore scholarship and a potential means for countering intergroup hostilities.
Indirect elicitation from ecological experts: From methods and software to habitat modelling and rock-wallabies
Authors: Tebaldi Claudia , Smith Richard
Published: August 2018

This article focuses on techniques for eliciting expert judgement about complex uncertainties, and more specifically the habitat of the Australian brush-tailed rock-wallaby. Modelling wildlife habitat requirements is important for mapping the distribution of the rock-wallaby, a threatened species, and therefore informing conservation and management. The Bayesian statistical modelling framework provides a useful ‘bridge’, from purely expert-defined models, to statistical models allowing survey data and expert knowledge to be ‘viewed as complementary, rather than alternative or competing, information sources’. The article describes the use of a rigorously designed and implemented expert elicitation for multiple experts, as well as a software tool for streamlining, automating and facilitating an indirect approach to elicitation. This approach makes it possible to infer the relationship between probability of occurrence and the environmental variables and demonstrates how expert knowledge can contribute to habitat modelling.
Volatility in prediction markets: A measure of information flow in political campaigns
Authors: Dawid A. Philip , Mortera Julia , Vicard Paola
Published: August 2018

This article discusses the use of Bayesian analysis in the evaluation of temporal volatility and information flows in political campaigns. Using the 2004 US presidential election campaign as a case study, it demonstrates the utility of a model with two volatility regimes that simplifies the task of associating events with periods of high information. The article first explains why prediction markets are able to aggregate information such that the prices of future contracts are reflective of the event’s actual probability of occurring before analysing data from futures on ‘Bush wins the popular vote in 2004’, or the traded probability, of Bush winning the election. These data are used to build a measure of information flow. The results show that information flows increased as a result of the televised debates, and that these debates, along with the selection of the vice presidential candidate, increased prediction market volatility.
Bayesian causal inference: Approaches to estimating the effect of treating hospital type on cancer survival in Sweden using principal stratification
Authors: Rubin Donald , Wang Xiaoqin , Yin Li , Zell Elizabeth
Published: August 2018

This article discusses the use of Bayesian causal inference, and more specifically the posterior predictive approach of Rubin’s causal model (RCM) and methods of principal stratification, in estimating the effects of ‘treating hospital type’ on cancer survival. Using the Karolinska Institute in Stockholm, Sweden, as a case study, the article investigates which type of hospital (large patient volume vs. small volume) is superior for treating certain serious conditions. The study examines which factors may reasonably be considered ignorable in the context of covariates available, as well as non-compliance complications due to transfers between hospital types for treatment. The article first provides an overview of the general Bayesian approach to causal inference, primarily with ignorable treatment assignment, before introducing the proposed approach and motivating it using simple method-of-moments summary statistics. Finally, the results of simulation using Markov chain Monte Carlo (MCMC) methods are presented.
Bayesian statistical methods for audio and music processing
Authors: Cemgil A. Taylan , Godsill Simon , Peeling Paul , Whiteley Nick
Published: August 2018

This article focuses on the use of Bayesian statistical methods in audio and music processing in the context of an application to multipitch audio and determining a musical ‘score’ representation that includes pitch and time duration summary for a musical extract (the so-called ‘piano-roll’ representation of music). It first provides an overview of mainstream applications of audio signal processing, the properties of musical audio, superposition and how to address it using the Bayesian approach, and the principal challenges facing audio processing. It then considers the fundamental audio processing tasks before discussing a range of Bayesian hierarchical models involving both time and frequency domain dynamic models. It shows that Bayesian analysis is applicable in audio signal processing in real environments where acoustical conditions and sound sources are highly variable, yet audio signals possess strong statistical structure.
Multistate models for mental fatigue
Authors: Prado Raquel
Published: August 2018

This article discusses the use of structured, multivariate Bayesian dynamic models in the analysis of experimental data involving large-scale electroencephalography (EEG) signals or time series generated on individuals subject to tasks inducing mental fatigue. It first provides an overview of the goals and challenges in the analysis of brain signals, using the EEG case as example, before describing the development and application of novel time-varying autoregressive and regime switching models, which incorporate relevant prior information via structured priors and fitted using novel, customized Bayesian computational methods. In the experiment, a subject was asked to perform simple arithmetic operations for a period of three hours. Prior to the experiment, the subject was confirmed to be alert. After the experiment ended, the subject was fatigued. The study demonstrates that Bayesian analysis is useful for real time detection of cognitive fatigue.
Sensitivity analysis in microbial risk assessment: Vero-cytotoxigenic E. coli O157 in farm-pasteurized milk
Authors: Oakley Jeremy E. , Clough Helen E.
Published: August 2018

This article discusses the use of Bayesian methods for performing uncertainty analysis in complex computer models, focusing on a mechanistic model that has been applied in a risk assessment of contamination of farm-pasteurized milk with the bacterium Vero-cytotoxigenic E. coli (VTEC) O157. The VTEC model has uncertain input parameters, which makes outputs from the model used to inform the risk assessment also uncertain. The question that arises is how to reduce output uncertainty in the most efficient manner possible. The article first provides an overview of microbial risk assessment before analysing the frequency and consequences of food-borne outbreaks associated with VTEC O157. It then introduces the risk assessment model, along with model input distributions. Finally, it presents the results of a variance-based sensitivity analysis that was conducted to identify the most important uncertain model inputs.
Mapping malaria in the Amazon rain forest: A spatio-temporal mixture model
Authors: Schmidt Alexandra , Hoeting Jennifer , Pereira João Batista M. , Vieira Pedro Paulo
Published: August 2018

This article focuses on the use of a spatio-temporal mixture model for mapping malaria in the Amazon rain forest. The spatio-temporal model was developed to study malaria outbreaks over a four year period in the state of Amazonas, Brazil. The goal is to predict malaria counts for unobserved municipalities and future time periods with the aid of a free-form spatial covariance structure and a methodology that allows temporal prediction and spatial interpolation for outbreaks of malaria over time. The proposed structure is unique in that it is not a distance- or neighbourhood-based covariance model. Instead, spatial correlation is allowed among all locations to be estimated freely. To model the temporal correlation between observations, a Bayesian dynamic linear model is incorporated into one level of the spatio-temporal mixture model. The model also provides sensible ways of malaria mapping for municipalities which were not observed.
Linking systems biology models to data: A stochastic kinetic model of p53 oscillations
Authors: Henderson Daniel A. , Boys R.J. , Proctor Carole J. , Wilkinson Darren J.
Published: August 2018

This article discusses the use of a stochastic kinetic model to study protein level oscillations in single living cancer cells, using the p53 and Mdm2 proteins as examples. It describes the refinement of a dynamic stochastic process model of the cellular response to DNA damage and compares this model to time course data on the levels of p53 and Mdm2. The article first provides a biological background on p53 and Mdm2 before explaining how the stochastic kinetic model is constructed. It then introduces the stochastic kinetic model and links it to the data and goes on to apply sophisticated MCMC methods to compute posterior distributions. The results demonstrate that it is possible to develop computationally intensive Markov chain Monte Carlo (MCMC) methods for conducting a Bayesian analysis of an intra-cellular stochastic systems biology model using single-cell time course data.
Heavy-tailed random matrices
Authors: Burda Zdzislaw , Jurkiewicz Jerzy
Published: August 2018

This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.
Two-matrix models and biorthogonal polynomials
Authors: Bertola Marco
Published: August 2018

This article considers two cases of two-matrix models that are amenable to biorthogonal polynomials: Itzykson-Zuber interaction and Cauchy interaction. The features and applications of the biorthogonal polynomials relevant to either case are discussed, but first the article provides an overview of chain-matrix models. It then describes the Itzykson-Zuber Hermitian two-matrix model and the Christoffel–Darboux identities, along with the spectral curve. It also examines the so-called mixed correlation functions that are involved in the combinatorial applications of the two-matrix model before concluding with an analysis of the Cauchy two-matrix model, which in a ‘complication scale’ turns out to lie in between the one-matrix model and the Itzykson-Zuber two-matrix model.
History – an overview
Authors: Bohigas Oriol , Weidenmuller Hans
Published: August 2018

This article discusses the first four decades of the history of random matrix theory (RMT), that is, until about 1990. It first considers Niels Bohr's formulation of the concept of the compound nucleus, which is at the root of the use of random matrices in physics, before analysing the development of the theory of spectral fluctuations. In particular, it examines the Wishart ensemble; Dyson's classification leading to the three canonical ensembles — Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE), and Gaussian Symplectic Ensemble (GSE); and the breaking of a symmetry or an invariance. It also describes how random matrix models emerged from quantum physics, more specifically from a statistical approach to the strongly interacting many-body system of the atomic nucleus. The article concludes with an overview of data on nuclear resonances, many-body theory, chaos, number theory, scattering theory, replica trick and supersymmetry, disordered solids, and interacting fermions and field theory.
Beta ensembles
Authors: Forrester Peter
Published: August 2018

This article deals with beta ensembles. Classical random matrix ensembles contain a parameter β, taking on the values 1, 2, and 4. This parameter, which relates to the underlying symmetry, appears as a repulsion sβ between neighbouring eigenvalues for small s. β may be regarded as a continuous positive parameter on the basis of different viewpoints of the eigenvalue probability density function for the classical random matrix ensembles - as the Boltzmann factor for a log-gas or the squared ground state wave function of a quantum many-body system. The article first considers log-gas systems before discussing the Fokker-Planck equation and the Calogero-Sutherland system. It then describes the random matrix realization of the β-generalization of the circular ensemble and concludes with an analysis of stochastic differential equations resulting from the case of the bulk scaling limit of the β-generalization of the Gaussian ensemble.
Number theory
Authors: Keating Jon , Snaith Nina
Published: August 2018

This article examines some of the connections between random matrix theory (RMT) and number theory, including the modelling of the value distributions of the Riemann zeta function and other L-functions as well as the statistical distribution of their zeros. Number theory has been used in RMT to address seemingly disparate questions, such as modelling mean and extreme values of the Riemann zeta function and counting points on curves. One thing in common among the applications of RMT to number theory is the L-function. The statistics of the critical zeros of these functions are believed to be related to those of the eigenvalues of random matrices. The article first considers the truth of the generalized Riemann hypothesis before discussing the values of the Riemann zeta function, the values of L-functions, and further areas of interest with respect to the connections between RMT and number theory
Enumeration of maps
Authors: Bouttier Jeremie
Published: August 2018

This article discusses the relationship between random matrices and maps, i.e. graphs drawn on surfaces, with particular emphasis on the one-matrix model and how it can be used to solve a map enumeration problem. It first provides an overview of maps and related objects, recalling the basic definitions related to graphs and defining maps as graphs embedded into surfaces before considering a coding of maps by pairs of permutations. It then examines the connection between matrix integrals and maps, focusing on the Hermitian one-matrix model with a polynomial potential and how the formal expansion of its free energy around a Gaussian point (quadratic potential) can be represented by diagrams identifiable with maps. The article also illustrates how the solution of the map enumeration problem can be deduced by means of random matrix theory (RMT). Finally, it explains how the matrix model result can be translated into a bijective proof.
Knot theory and matrix integrals
Authors: Zinn-Justin Paul , Zuber Jean-Bernard
Published: August 2018

This article considers some enumeration problems in knot theory, with a focus on the application of matrix integral techniques. It first reviews the basic definitions of knot theory, paying special attention to links and tangles, especially 2-tangles, before discussing virtual knots and coloured links as well as the bare matrix model that describes coloured link diagrams. It shows how the large size limit of matrix integrals with quartic potential may be used to count alternating links and tangles. The removal of redundancies amounts to renormalization of the potential. This extends into two directions: first, higher genus and the counting of ‘virtual’ links and tangles, and second, the counting of ‘coloured’ alternating links and tangles. The article analyses the asymptotic behaviour of the number of tangles as the number of crossings goes to infinity
Algebraic geometry and matrix models
Authors: Chekhov Leonid
Published: August 2018

This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants.
Two-dimensional quantum gravity
Authors: Kostov Ivan
Published: August 2018

This article discusses the connection between large N matrix models and critical phenomena on lattices with fluctuating geometry, with particular emphasis on the solvable models of 2D lattice quantum gravity and how they are related to matrix models. It first provides an overview of the continuum world sheet theory and the Liouville gravity before deriving the Knizhnik-Polyakov-Zamolodchikov scaling relation. It then describes the simplest model of 2D gravity and the corresponding matrix model, along with the vertex/height integrable models on planar graphs and their mapping to matrix models. It also considers the discretization of the path integral over metrics, the solution of pure lattice gravity using the one-matrix model, the construction of the Ising model coupled to 2D gravity discretized on planar graphs, the O(n) loop model, the six-vertex model, the q-state Potts model, and solid-on-solid and ADE matrix models.
String theory
Authors: Marino Marcos
Published: August 2018

This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds and states the Dijkgraaf–Vafa correspondence, focusing on how it is connected to string dualities and how it can be used to compute superpotentials in certain supersymmetric gauge theories. In addition, it shows how the correspondence extends to toric manifolds and leads to a matrix model approach to enumerative geometry. Finally, it reviews matrix quantum mechanics and its applications in superstring theory.
Quantum chromodynamics
Authors: Verbaarschot Jac
Published: August 2018

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.
Quantum chaos and quantum graphs
Authors: Muller Sebastian , Sieber Martin
Published: August 2018

This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’s periodic orbit theory and a refined approach incorporating the unitarity of the quantum evolution — and highlights their importance in understanding universal spectral statistics, and how they are related to the sigma model. This is followed by an analysis of parallel developments for quantum graphs, which are relevant to quantum chaos.
Resonance scattering of waves in chaotic systems
Authors: Fyodorov Yan , Savin Dmitry
Published: August 2018

This article discusses some applications of random matrix theory (RMT) to quantum or wave chaotic resonance scattering. It first provides an overview of selected topics on universal statistics of resonances and scattering observables, with emphasis on theoretical results obtained via non-perturbative methods starting from the mid-1990s. It then considers the statistical properties of scattering observables at a given fixed value of the scattering energy, taking into account the maximum entropy approach as well as quantum transport and the Selberg integral. It also examines the correlation properties of the S-matrix at different values of energy and concludes by describing other characteristics and applications of RMT to resonance scattering of waves in chaotic systems, including those relating to time delays, quantum maps and sub-unitary random matrices, and microwave cavities at finite absorption.
Condensed matter physics
Authors: Beenakker Carlo W. J.
Published: August 2018

This article discusses some applications of concepts from random matrix theory (RMT) to condensed matter physics, with emphasis on phenomena, predicted or explained by RMT, that have actually been observed in experiments on quantum wires and quantum dots. These observations range from universal conductance fluctuations (UCF) to weak localization, non-Gaussian thermopower distributions, and sub-Poissonian shot noise. The article first considers the UCF phenomenon, nonlogarithmic eigenvalue repulsion, and sub-Poissonian shot noise in quantum wires before analysing level and wave function statistics, scattering matrix ensembles, conductance distribution, and thermopower distribution in quantum dots. It also examines the effects (not yet observed) of superconductors on the statistics of the Hamiltonian and scattering matrix.
Classical and quantum optics
Authors: Beenakker Carlo W. J.
Published: August 2018

This article focuses on applications of random matrix theory (RMT) to both classical optics and quantum optics, with emphasis on optical systems such as disordered wave guides and chaotic resonators. The discussion centres on topics that do not have an immediate analogue in electronics, either because they cannot readily be measured in the solid state or because they involve aspects (such as absorption, amplification, or bosonic statistics) that do not apply to electrons. The article first considers applications of RMT to classical optics, including optical speckle and coherent backscattering, reflection from an absorbing random medium, long-range wave function correlations in an open resonator, and direct detection of open transmission channels. It then discusses applications to quantum optics, namely: the statistics of grey-body radiation, lasing in a chaotic cavity, and the effect of absorption on the reflection eigenvalue statistics in a multimode wave guide.
Extreme eigenvalues of Wishart matrices: application to entangled bipartite system
Authors: Majumdar Satya N.
Published: August 2018

This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.
Random growth models
Authors: Ferrari Patrik L. , Spohn Herbert
Published: August 2018

This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.
Random matrices and Laplacian growth
Authors: Zabrodin Anton
Published: August 2018

This article reviews the theory of random matrices with eigenvalues distributed in the complex plane and more general ‘beta ensembles’ (logarithmic gases in 2D). It first considers two ensembles of random matrices with complex eigenvalues: ensemble C of general complex matrices and ensemble N of normal matrices. In particular, it describes the Dyson gas picture for ensembles of matrices with general complex eigenvalues distributed on the plane. It then presents some general exact relations for correlation functions valid for any values of N and β before analysing the distribution and correlations of the eigenvalues in the large N limit. Using the technique of boundary value problems in two dimensions and elements of the potential theory, the article demonstrates that the finite-time blow-up (a cusp–like singularity) of the Laplacian growth with zero surface tension is a critical point of the normal and complex matrix models.
Spectral statistics of unitary ensembles
Authors: Anderson Greg W.
Published: August 2018

This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.
Spectral statistics of orthogonal and symplectic ensembles
Authors: Adler Mark
Published: August 2018

This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels
Universality
Authors: Kuijlaars Arno
Published: August 2018

This article deals with the universality of eigenvalue spacings, one of the basic characteristics of random matrices. It first discusses the heuristic meaning of universality before describing the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and symplectic ensembles. It then examines unitary matrix ensembles in more detail and shows that universality in these ensembles comes down to the convergence of the properly scaled eigenvalue correlation kernels. It also analyses the Riemann–Hilbert method, along with certain non-standard universality classes that arise at singular points in the limiting spectrum. Finally, it considers the limiting kernels for each of the three types of singular points, namely interior singular points, singular edge points, and exterior singular points.
Supersymmetry
Authors: Guhr Thomas
Published: August 2018

This article examines conceptual and structural issues related to supersymmetry. It first provides an overview of generating functions before discussing supermathematics, with a focus on Grassmann or anticommuting variables, vectors and matrices, groups and symmetric spaces, and derivatives and integrals. It then considers various applications of supersymmetry to random matrices, such as the representation of the ensemble average and the Hubbard–Stratonovich transformation, along with its generalization and superbosonization. It also describes matrix δ functions and an alternative representation as well as important and technically challenging problems that supersymmetry addresses beyond the invariant and factorizing ensembles. The article concludes with an analysis of the supersymmetric non-linear σ model, Brownian motion in superspace, circular ensembles and the Colour-Flavour-Transformation.
Replica approach in random matrix theory
Authors: Kanzieper Eugene
Published: August 2018

This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.
The World Historical Significance of European Legal History
Authors: Whitman James Q.
Published: August 2018

This chapter surveys some of the claims that scholars have made about the supposed world-historical significance of European legal history. Many authors, beginning with Montesquieu, have maintained that the rule of law is somehow a Western invention. Others, including Weber and many prominent contemporary economists, among them the Nobel Prize winner Douglass North, have insisted that peculiarly forms of law fostered the rise of modern capitalism. There is even a tradition of praise for the special value of Western law among biologists, dating back to Linnaeus. The chapter calls on professional legal historians to address these various grand claims about European legal history seriously, and offers some tentative responses to them.
Feudal Law
Authors: Heirbaut Dirk
Published: August 2018

Historians of a previous generation saw feudalism as a creation of the Carolingians, which was to be found mainly in the heartland of their empire. However, in 1994 Susan Reynolds demolished this view: feudalism is not medieval, but the product of the early modern era, albeit with roots in the medieval Libri Feudorum. Reynolds and others were right in attacking the old views but, on the other hand, recent research also shows that in at least four pioneering regions feudalism already appears in the eleventh century, before the Libri Feudorum. However, the latter helped to spread feudalism to other parts of Europe. The upshot was not one model of feudalism that was slavishly followed all over Europe and remained constant until the demise of feudalism. There were only regional feudalisms that were very different from the model of the traditional handbooks.
Western Canon Law in the Central and Later Middle Ages
Authors: Clarke Peter
Published: August 2018

This chapter explores a significant period in the formation, teaching, and application of canon law. Firstly, it marked the emergence of a universal body of Western canon law which remained in force among Catholics down to 1917; and the chapter will survey recent scholarly debate about the development of this corpus of canon law. Secondly, universities appeared and established the systematic teaching and study of canon (and civil) law. Canon law collections were often compiled in this milieu, and university teachers produced commentaries and other literature on this law, which influenced how it was interpreted and applied in practice. Thirdly, regular church courts emerged across Western Europe as forums for settling disputes and prosecuting crimes that came under canon law. These courts formed an international hierarchy with the papal Curia at its apex, the highest ecclesiastical court of appeal, and stretching down to bishops’ and archdeacons’ courts at diocesan level.