entanglement entropy from corner transfer matrix in forrester baxter non unitary rsos models using a corner transfer matrix approach we compute the bipartite entanglement renyi entropy in the off critical perturbations of non unitary conformal minimal models realised by lattice spin chains hamiltonians related to the forrester baxter rsos models bianchini et al 2015 j stat mech p03010 in regime iii this allows to show on a set of explicit examples that the renyi entropies for non unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge this complements a similar result recently established for the size rescaling at the critical point bianchini et al 2015 j phys a math theor 48 04ft01 showing the expected agreement of the two behaviours we also compute the first subleading unusual correction to the scaling behaviour showing that it is expressible in terms of expansions of various fractional powers of the correlation length related to the differences between the conformal dimensions of fields in the theory and the minimal conformal dimension finally a few observations on the limit leading to the off critical logarithmic minimal models of pearce and seaton 2012 j stat mech p09014 are put forward

on the elliptic 2 solid on solid model functional relations and determinants in this work we study an elliptic solid on solid model with domain wall boundaries having the elliptic quantum group ep gl2 as its underlying symmetry algebra we elaborate on results previously presented in galleas phys rev e 94 010102 2016 and extend our analysis to include continuous families of single determinantal representations for the model s partition function interestingly our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function in this work we study an elliptic solid on solid model with domain wall boundaries having the elliptic quantum group ep gl2 as its underlying symmetry algebra we elaborate on results previously presented in galleas phys rev e 94 010102 2016 and extend our analysis to include continuous families of single determinantal representations for the model s partition function interestingly our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function

height probabilities in solid on solid models i for pt i see ibid vol 19 p l923 1986 the rsos 3 model is a sequence of two dimensional solid on solid models with integer heights restricted between 1 and r 1 and nearest neighbours differing by 0 1 or 1 it has an exact solution manifold with four regimes of distinct physical behaviour along which the height probabilities in the bulk of the system can be calculated using some results of the previous letter in this series the authors calculate the height probabilities for two of the regimes appropriate order parameters are defined and their critical exponents calculated

exact operator solution of the calogero sutherland model the wave functions of the calogero sutherland model are known to be expressible in terms of jack polynomials a formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived the creation operators that enter in this formula of rodrigues type for the jack polynomials involve dunkl operators

finitized conformal spectrum of the ising model on the cylinder and torus abstract the spectrum of the critical ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods using a simple truncation procedure we obtain the natural finitizations of the conformal spectra recently proposed by melzer these finitizations imply polynomial identities which in the large lattice limit give rise to the rogers ramanujan identities for the c 1 2 virasoro characters

removable lateral singularities of semilinear parabolic pdes and besov capacities suppose 1 2 lis a second order elliptic differential operator in rdanddis a bounded smooth domain in rd let q r dand let be a compact set on the lateral boundary of q we prove that is a removable lateral singularity for the equationu lu u in q if and only if cap1 2 0 where cap stands for the besov capacity on the boundary

paths and partitions combinatorial descriptions of the parafermionic states the zk parafermionic conformal field theories despite the relative complexity of their modes algebra offer the simplest context for the study of the bases of states and their different combinatorial representations three bases are known the classic one is given by strings of the fundamental parafermionic operators whose sequences of modes are in correspondence with restricted partitions with parts at distance k 1 differing at least by 2 another basis is expressed in terms of the ordered modes of the k 1 different parafermionic fields which are in correspondence with the so called multiple partitions both types of partitions have a natural bressoud path representation finally a third basis formulated in terms of different paths is inherited from the solution of the restricted solid on solid model of andrews baxter forrester the aim of this work is to review in a unified and pedagogical exposition these four different combinatorial representations of the states of the zk parafermionic models

a monomial basis for the virasoro minimal series m p p the case 1 p p 2 quadratic relations are given explicitly in two cases of chiral conformal field theory and monomial bases of the representation spaces are constructed by using the fourier components of the intertwiners the first case is the 2 1 primary fields for the p p minimal series m r s 1 r p 1 1 s p 1 for the virasoro algebra where 1 p p 2 we restrict ourselves to the case p 3 for which the 2 1 primary field exists the second case is the intertwiners corresponding to the two dimensional representation for the level k integrable highest weight modules v 0 k for the affine lie algebra open image in new window

robust stochastic approximation approach to stochastic programming in this paper we consider optimization problems where the objective function is given in a form of the expectation a basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals expectations cannot be computed with high accuracy the aim of this paper is to compare two computational approaches based on monte carlo sampling techniques namely the stochastic approximation sa and the sample average approximation saa methods both approaches the sa and saa methods have a long history current opinion is that the saa method can efficiently use a specific say linear structure of the considered problem while the sa approach is a crude subgradient method which often performs poorly in practice we intend to demonstrate that a properly modified sa approach can be competitive and even significantly outperform the saa method for a certain class of convex stochastic problems we extend the analysis to the case of convex concave stochastic saddle point problems and present in our opinion highly encouraging results of numerical experiments

integrable boundaries conformal boundary conditions and a d e fusion rules the sl 2 minimal theories are classified by a lie algebra pair where g is of a d e type for these theories on a cylinder we propose a complete set of conformal boundary conditions labelled by the nodes of the tensor product graph the cylinder partition functions are given by fusion rules arising from the graph fusion algebra of we further conjecture that for each conformal boundary condition an integrable boundary condition exists as a solution of the boundary yang baxter equation for the associated lattice model the theory is illustrated using the or three state potts model

the brownian snake and solutions of δu u2 in a domain we investigate the connections between the path valued process called the brownian snake and nonnegative solutions of the partial differential equation u u2 in a domain of d in particular we prove two conjectures recently formulated by dynkin the first one gives a complete characterization of the boundary polar sets which correspond to boundary removable singularities for the equation u u2 the second one establishes a one to one correspondence between nonnegative solutions that are bounded above by a harmonic function and finite measures on the boundary that do not charge polar sets this correspondence can be made explicit by a probabilistic formula involving a special class of additive functionals of the brownian snake our proofs combine probabilistic and analytic arguments an important role is played by a new version of the special markov property which is of independent interest

fermionic solution of the andrews baxter forrester model i unification of tba and ctm methods the problem of computing the one dimensional configuration sums of the abf model in regime iii is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged particles obeying certain fermionic exclusion rules we thus obtain a newfermionic method to compute the local height probabilities of the model combined with the originalbosonic approach of andrews baxter and forrester we obtain a new proof of some of melzer s polynomial identities in the infinite limit these identities yield rogers ramanujan type identities for the virasoro characters l 1 r l r q as conjectured by the stony brook group as a result of our work the corner transfer matrix and thermodynamic bethe ansatz approaches to solvable lattice models are unified

exact calculation of the local height probabilities in the body centred sos model the local height probabilities pa and the mean square height average h2 are calculated exactly for the smooth phase of the body centred solid on solid model near criticality pa approximately k t 1 4 and h2 approximately k t 1 2 where t is the deviation from criticality parameter and k k are constants specified in the text

q trinomial identities we obtain connection coefficients between q binomial and q trinomial coefficients using these one can transform q binomial identities into q trinomial identities and back again to demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of berkovich mccoy and pearce which have recently arisen in their study of the 2 1 and 1 5 perturbations of minimal conformal field theory

rogers ramanujan identities in the hard hexagon model the hard hexagon model in statistical mechanics is a special case of a solvable class of hard square type models in which certain special diagonal interactions are added the sublattice densities and order parameters of this class are obtained and it is shown that many rogers ramanujan type identities naturally enter the working

some combinatorial properties of jack symmetric functions if 1 l n then write 2 n or 1 n if p is another partition then write p c j if pi 6 for all i i e if the diagram of 1 contains the diagram of p if ipl ii 1 then write p 2 1 reverse lexicographic order if either j i or the first nonvanishing difference e pi is positive for instance writing 2 1 i for ai i it 5 5 41 32 5 311 221 2111 11111 finally write p i if ipl lal and p1 pl2 pli a1 a2 li for all i macdonald m p 63 call the partial ordering the natural ordering but we will call it the dominance ordering let x x x2 be an infinite set of indeterminates as in mi we

proof of the flohr grabow koehn conjectures for characters of logarithmic conformal field theory in a recent paper flohr grabow and koehn conjectured that the characters of the logarithmic conformal field theory ck 1 admit fermionic representations labelled by the lie algebra dk in this paper we provide a simple analytic proof of this conjecture

false theta functions and companions to capparelli s identities abstract capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions which were motivated by the calculation of characters for the standard modules of certain affine lie algebras and by vertex operator theory these identities were subsequently proved and refined by andrews who related them to jacobi theta functions and also by alladi andrews gordon capparelli and tamba xie in this paper we prove two new companions to capparelli s identities where the evaluations are expressed in terms of jacobi theta functions and false theta functions

the andrews gordon identities and q multinomial coefficients we prove polynomial boson fermion identities for the generating function of the number of partitions of n of the form n sum j 1 l 1 j f j with f 1 leq i 1 f l 1 leq i 1 and f j f j 1 leq k the bosonic side of the identities involves q deformations of the coefficients of x a in the expansion of 1 x cdots x k l a combinatorial interpretation for these q multinomial coefficients is given using durfee dissection partitions the fermionic side of the polynomial identities arises as the partition function of a one dimensional lattice gas of fermionic particles

fermionic solution of the andrews baxter forrester model ii proof of melzer s polynomial identities we compute the one dimensional configuration sums of the abf model using the fermionic technique introduced in part i of this paper combined with the results of andrews baxter and forrester we prove polynomial identities for finitizations of the virasoro characters chi b a r 1 r q as conjectured by melzer in the thermodynamic limit these identities reproduce rogers ramanujan type identities for the unitary minimal virasoro characters conjectured by the stony brook group we also present a list of additional virasoro character identities which follow from our proof of melzer s identities and application of bailey s lemma

a new family of algebras underlying the rogers ramanujan identities and generalizations abstract the classical rogers ramanujan identities have been interpreted by lepowsky milne and the present authors in terms of the representation theory of the euclidean kac moody lie algebra a1 1 also the present authors have introduced certain vertex differential operators providing a construction of a1 1 on its basic module and kac kazhdan and we have generalized this construction to a general class of euclidean lie algebras starting from this viewpoint we now introduce certain new algebras unk v which centralize the action of the principal heisenberg subalgebra of an arbitrary euclidean lie algebra unk on a highest weight unk module v we state a general tautological rogers ramanujan type identity which by our earlier theorem includes the classical identities and we show that unk v can be used to reformulate the general identity for unk a1 1 we develop the representation theory of unk v in considerable detail allowing us to prove our earlier conjecture that our general rogers ramanujan type identity includes certain identities of gordon andrews and bressoud in the process we construct explicit bases of all of the standard and verma modules of nonzero level for a1 1 with an explicit realization of a1 1 as operators in each case the differential operator constructions mentioned above correspond to the trivial case unk v 1 of the present theory

solvable models in statistical mechanics from onsager onward there is now a whole field in mathematical physics concerned with solvable models in statistical mechanics field theory and related areas we indicate the influence that onsager s solution of the planar ising model has had and continues to have on this field

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

further exact solutions of the eight vertex sos model and generalizations of the rogers ramanujan identities the restricted eight vertex solid on solid sos model is an exactly solvable class of two dimensional lattice models to each sitei of the lattice there is associated an integer heightli restricted to the range 1 li r 1 the boltzmann weights of the model are expressed in terms of elliptic functions of period 2k and involve a parameter in an earlier paper we considered the case k r here we generalize those considerations to the case sk r s an integer relatively prime tor we are again led to generalizations of the rogers ramanujan identities

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

introduction to convex optimization in financial markets convexity arises naturally in financial risk management in risk preferences concerning random cash flows convexity corresponds to the fundamental diversification principle convexity is a basic property also of budget constraints both in classical linear models as well as in more realistic models with transaction costs and constraints moreover modern securities markets are based on trading protocols that result in convex trading costs the first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simple optimization terms the second part reviews some convex optimization techniques used in mathematical and numerical analysis of financial optimization problems

construction of modular branching functions from bethe s equations in the 3 state potts chain in the present work the authors use the single particle excitation energies and the completeness rules of the 3 state antiferromagnetic potts chain which have been obtained from bethe s equation to compute the modular invariant partition function this provides a fermionic construction for the branching functions of the d sub 4 representation of z sub 4 parafermions which complements the bosonic constructions it is found that there are oscillations in some of the correlations and a new connection with the field theory of the lee yang edge is presented 47 refs 9 tabs

particles in rsos paths we introduce a new representation of the paths of the forrester baxter restricted solid on solid rsos models which represents the states of the irreducible modules of the minimal models this representation is obtained by transforming the rsos paths for the cases p 2p 1 to new paths for which horizontal edges are allowed at certain heights these new paths are much simpler in that their weight is nothing but the sum of the position of the peaks this description paves the way for the interpretation of the rsos paths in terms of fermi type charged particles out of which the fermionic characters could be obtained constructively the derivation of the fermionic character for p 2 and p kp 1 is outlined finally the particles of the rsos paths are put in relation to the kinks and the breathers of the restricted sine gordon model

parafermionic derivation of andrews type multiple sums a multi parafermion basis of states for the parafermionic models is derived its generating function is constructed by elementary steps it corresponds to the andrews multiple sum which enumerates partitions whose parts separated by the distance k 1 differ by at least 2 two analogous bases are derived for graded parafermions one of these entails a new expression for their fermionic characters

optimal consumption from investment and random endowment in incomplete semimartingale markets we consider the problem of maximizing expected utility from consumption in a con strained incomplete semimartingale market with a random endowment process and establish a general existence and uniqueness result using techniques from convex duality the notion of as ymptotic elasticity of kramkov and schachermayer is extended to the time dependent case by imposing no smoothness requirements on the utility function in the temporal argument we can treat both pure consumption and combined consumption terminal wealth problems in a com mon framework to make the duality approach possible we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of l 1 to its topological bidual l 1 a space of finitely additive measures as an application we treat a constrained ito process market model as well as a totally incomplete model

a nonlocal operator basis from the path representation of the cal m k 1 hbox k 2 and the cal m k 1 hbox 2k 3 minimal models we reinterpret a path describing a state in an irreducible module of the unitary minimal model in terms of a string of charged operators acting on the module s ground state path each such operator acts non locally on a path the path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis as an application we re derive the vacuum finite fermionic character by constructing the generating function of these basis states these results generalize directly to the models the close relatives of the unitary models in terms of path description

on the equation δu eu 1 0 with measures as boundary data if is a bounded domain in mathbb r n we study conditions on a radon measure on for solving the equation u e u 1 0 in with u on the conditions are expressed in terms of orlicz capacities

exceptional structure of the dilute a 3 model e 8 and e 7 rogers ramanujan identities the dilute a3 lattice model in regime 2 is in the universality class of the ising model in a magnetic field here we directly establish the existence of an e8 structure in the dilute a3 model in this regime by expressing the one dimensional configuration sums in terms of fermionic sums which involve the e8 root system explicitly in the thermodynamic limit these polynomial identities yield a proof of the e8 rogers ramanujan identity recently conjectured by kedem et al 1993 the polynomial identities also apply to regime 3 which is obtained by transforming the modular parameter by q to 1 q in this case we find an a1xe7 structure and prove a rogers ramanujan identity of a1xe7 type finally in the critical q to 1 limit we give some intriguing expressions for the number of l step paths on the a3 dynkin diagram with tadpoles in terms of the e8 cartan matrix all our findings confirm the e8 and e7 structure of the dilute a3 model found recently by means of the thermodynamic bethe ansatz

graphical approach to the nonintersecting string model star triangle equation inversion relation and exact solution abstract a general q state nonintersecting string model for q 2 is studied and solved using a graphical approach this model of which special cases were first introduced by strogonov and schultz has recently drawn further attention because of its relation to potts models in its simplest version a uniform separable nonintersecting string model on a quadratic lattice it corresponds to a q2 state potts model with potts spins on every other lattice face we first formulate the related star triangle equation which we solve in terms of a line variable parametrization such a parametrization of a solution of the star triangle equation leads to a simple and direct graphical derivation of an inversion relation for the partition function our graphical analysis also shows that the inversion relation holds if certain boundary effects can be neglected as we shall give a special finite lattice from which the inversion relation can be read off immediately this relation is next solved under appropriate analyticity assumptions again using a simple and direct approach and the result is applied to obtain exact solutions for specific string models

solutions of semilinear differential equations related to harmonic functions this is an attempt to establish a link between positive solutions of semilinear equations lu u and lv v where l is a second order elliptic differential operator and is a positive function the equations were investigated separately by a number of authors we try to link them via positive solutions of a linear equation lu 0 we call them l harmonic functions let d be an arbitrary open subset of rd and let u d v d and h d stand for the sets of all positive solutions in d for three equations mentioned above we establish a 1 1 correspondence between certain subclasses of these classes similar results are obtained also for the corresponding parabolic equations a probabilistic interpretation in terms of a superdiffusion is given in 1

entanglement entropy of non unitary conformal field theory here we show that the renyi entanglement entropy of a region of large size l in a one dimensional critical model whose ground state breaks conformal invariance such as in those described by non unitary conformal field theories behaves as ceff n 1 2n log l where ceff c 24delta 0 is the effective central charge c which may be negative is the central charge of the conformal field theory and delta 0 is the lowest holomorphic conformal dimension in the theory we also obtain results for models with boundaries and with a large but finite correlation length and we show that if the lowest conformal eigenspace is logarithmic then there is an additional term proportional to log log l these results generalize the well known expressions for unitary models we provide a general proof and report on numerical evidence for a non unitary spin chain and an analytical computation using the corner transfer matrix method for a non unitary lattice model we use a new algebraic technique for studying the branching that arises within the replica approach and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non unitary models

rogers schur ramanujan type identities for the m p p minimal models of conformal field theory we present and prove rogers schur ramanujan bose fermi type identities for the virasoro characters of the minimal model m p p the proof uses the continued fraction decomposition of p p introduced by takahashi and suzuki for the study of the bethe s ansatz equations of the xxz model and gives a general method to construct polynomial generalizations of the fermionic form of the characters which satisfy the same recursion relations as the bosonic polynomials of forrester and baxter we use this method to get fermionic representations of the characters for many classes of r and s

from path representations to global morphisms for a class of minimal models we construct global observable algebras and global dhr morphisms for the virasoro minimal models with central charge c 2 q q odd to this end we pass from the irreducible highest weight modules to path representations which involve fusion graphs of the c 2 q models the paths have an interpretation in terms of quasi particles which capture some structure of non conformal perturbations of the c 2 q models the path algebras associated to the path spaces serve as algebras of bounded observables global morphisms which implement the superselection sectors are constructed using quantum symmetries we argue that there is a canonical semi simple quantum symmetry algebra for each quasi rational cft in particular for the c 2 q models these symmetry algebras act naturally on the path spaces which allows to define a global field algebra and covariant multiplets therein

further solutions of critical abf rsos models the restricted sos model of andrews baxter and forrester 1984 has been studied the finite size corrections to the eigenvalue spectra of the transfer matrix of the model with a more general crossing parameter have been calculated therefore the conformal weights and the central charges of the non unitary or unitary minimal conformal field have been extracted from the finite size corrections

stochastic boundary values and boundary singularities for solutions of the equationlu uα abstract we investigate positive solutions of a nonlinear equationlu u wherelis a second order elliptic differential operator in a riemannian manifoldeand 1 2 we establish a 1 1 correspondence between the set u of positive solutions and a class z of functionals ofxwhich we call linear boundary functionals they depend only on the behavior ofxnear the martin boundarye the class z is a closed convex cone andu u is a subadditive function ofz z special roles belong to moderate solutions corresponding tozwith finite mathematical expectations and to a family of solutions determined by the range ofx a new formula is deduced connectingu zandl diffusions conditioned to hit the boundarye at a given pointy a concept of a singular boundary point foruis introduced in terms of the conditioned diffusion

stochastic equilibria in von neumann gale dynamical systems this paper examines a class of random dynamical systems related to the classical von neumann and gale models of economic dynamics such systems are defined in terms of multivalued operators in spaces of random vectors possessing certain properties of convexity and homogeneity we establish a general existence theorem for equilibrium which holds under conditions analogous to the standard deterministic ones our results answer questions that remained open for more than three decades

log optimal and rapid paths in von neumann gale dynamical systems abstract von neumann gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors possessing certain properties of convexity and homogeneity a central role in the theory of such systems is played by a special class of paths trajectories called rapid they grow over each time period t 1 t in a sense faster than others the paper establishes existence and characterization theorems for such paths showing in particular that any trajectory maximizing a logarithmic functional over a finite time horizon is rapid the proof of this result is based on the methods of convex analysis in spaces of measurable functions the study is motivated by the applications of the theory of von neumann gale dynamical systems to the modeling of capital growth in financial markets with friction

a probabilistic approach to one class of nonlinear differential equations we establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes as an application we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations

the emerging role of number theory in exactly solvable models in lattice statistical mechanics abstract we review the baxter model the hard hexagon model and their multistate generalizations from a point of view that stresses the connection with modular functions and additive number theory it is shown for example that various physical quantities in the hard hexagon model are all expressible in terms of modular functions the use of rogers ramanujan type identities in solvable models is also reviewed

the rogers ramanujan identities lie theoretic interpretation and proof abstract the two rogers ramanujan identities which equate certain infinite products with infinite sums are among the most intriguing of the classical formal power series identitites it has been found by lepowsky and milne that the product side of each of them differs by a certain factor from the principally specialized character of a certain standard module for the euclidean kac moody lie algebra a1 1 on the other hand the present authors have introduced an infinite dimensional heisenberg subalgebra unk of a1 1 which leads to a construction of a1 1 in terms of differential operators given by the homogeneous components of an exponential generating function in the present announcement we use unk to formulate a natural abstract rogers ramanujan identity for an arbitrary standard a1 1 module which turns out to coincide with the classical identities in the cases of the two corresponding standard modules the abstract identity equates two expressions one a product and the other a sum for the principally specialized character of the space of highest weight vectors or vacuum states for unk in the module the construction of a1 1 leads to a concrete realization of as the span of certain spaces of symmetric polynomials occurring as the homogeneous components of exponential generating functions the summands in the rogers ramanujan identities turn out to count the dimensions of these spaces for general standard a1 1 modules we conjecture that the abstract identities agree with generalizations of the rogers ramanujan identities due to gordon andrews and bressoud

shadow price of information in discrete time stochastic optimization the shadow price of information has played a central role in stochastic optimization ever since its introduction by rockafellar and wets in the mid seventies this article studies the concept in an extended formulation of the problem and gives relaxed sufficient conditions for its existence we allow for general adapted decision strategies which enables one to establish the existence of solutions and the absence of a duality gap e g in various problems of financial mathematics where the usual boundedness assumptions fail as applications we calculate conjugates and subdifferentials of integral functionals and conditional expectations of normal integrands we also give a dual form of the general dynamic programming recursion that characterizes shadow prices of information

convex duality in stochastic optimization and mathematical finance this paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration the framework unifies many well known duality frameworks from operations research and mathematical finance the unification allows the extension of some useful techniques from these two fields to a much wider class of problems in particular combining certain finite dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance we are able to close the duality gap in some situations where traditional topological arguments fail

convex duality in optimal investment under illiquidity we study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis this allows for various extensions to classical models of liquid markets in particular we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e g in modern limit order markets the optimization problem is parameterized by a sequence of financial claims such a parameterization is essential in markets without a numeraire asset when pricing swap contracts and other financial products with multiple payout dates in the special case of perfectly liquid markets or markets with proportional transaction costs we recover well known dual expressions in terms of martingale measures

q trinomial coefficients and the dilute a model we express the configuration sums of the dilute model in regimes and in terms of q trinomial coefficients we then extend previous results to give expressions for all phases and regimes for odd l for finite system size

stochastic programs without duality gaps this paper studies dynamic stochastic optimization problems parameterized by a random variable such problems arise in many applications in operations research and mathematical finance we give sufficient conditions for the existence of solutions and the absence of a duality gap our proof uses extended dynamic programming equations whose validity is established under new relaxed conditions that generalize certain no arbitrage conditions from mathematical finance

removable singularities for lu ψ u and orlicz capacities suppose l is a second order elliptic differential operator in rd and let 1 baras and pierre have proved in 1984 that is removable for lu u if and only if its bessel capacity cap2 0 we extend this result to a general equation lu u where u is an increasing convex function subject to 2 and 2 conditions namely we prove that is removable for lu u if and only if its orlicz capacity is zero that is the integral b dx x y 2 d dy is equal to 0 or for every measure concentrated on where b stands for any ball containing

polynomial identities indices and duality for the n 1 superconformal model sm 2 4v we prove polynomial identities for then 1 superconformal modelsm 2 4v which generalize and extend the known fermi bose character identities our proof uses theq trinomial coefficients of andrews and baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq series on the fermionic side we use these polynomials to demonstrate a dual relation underq q 1 betweensm 2 4v andm 2v 1 4v we also introduce a genralization of the witten index which is expressible in terms of the rogers false theta functions

a functional version of the birkhoff ergodic theorem for a normal integrand a variational approach in this paper we prove a new version of the birkhoff ergodic theorem bet for random variables depending on a parameter alias integrands this involves variational convergences namely epigraphical hypographical and uniform convergence and requires a suitable definition of the conditional expectation of integrands we also have to establish the measurability of the epigraphical lower and upper limits with respect to the field of invariant subsets from the main result applications to uniform versions of the bet to sequences of random sets and to the strong consistency of estimators are briefly derived

boundary conformal field theories and loop models we propose a systematic method to extract conformal loop models for rational conformal field theories cft the method is based on defining an ade model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices these loop models respect the conformal boundary conditions we discuss the loop models that can be extracted by this method for minimal cfts and then we give dilute o n loop models on the square lattice as examples for these loop models we also give some proposals for wzw su 2 models

n 2 supersymmetry and bailey pairs abstract we demonstrate that the bailey pair formulation of rogers ramanujan identities unifies the calculations of the characters of n 1 and n 2 supersymmetric conformal field theories with the counterpart theory with no supersymmetry we illustrate this construction for the m 3 4 ising model where the bailey pairs have been given by slater we then present the general unitary case we demonstrate that the model m p p 1 is derived from m p 1 p by a bailey renormalization flow and conclude by obtaining the n 1 model sm p p 2 and the unitary n 2 model with central charge c 3 1 2 p

local height probabilities in a composite andrews baxter forrester model we study the local height probabilities in a composite height model derived from the restricted solid on solid model introduced by andrews baxter and forrester and their connection with conformal field theory characters the obtained conformal field theories also describe the critical behavior of the model at two different critical points in addition at criticality the model is equivalent to a one dimensional chain of anyons subject to competing two and three body interactions the anyonic chain interpretation provided the original motivation to introduce the composite height model and by obtaining the critical behavior of the composite height model the critical behavior of the anyonic chains is established as well depending on the overall sign of the hamiltonian this critical behavior is described by a diagonal coset model generalizing the minimal models for one sign and by fateev zamolodchikov parafermions for the other

convex duality in nonlinear optimal transport abstract this article studies problems of optimal transport by embedding them in a general functional analytic framework of convex optimization this provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations general results on convex duality yield dual problems and optimality conditions for these problems when the objective takes the form of a convex integral functional we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem this covers in particular the mass transportation problem and its nonlinear generalizations

a probabilistic approach to the equation lu u2 let l be a second order elliptic differential operator and let d be an arbitrary open subset of rd in 1 we introduced a class u1 d of positive solutions of the equation lu u2 which is in 1 1 correspondence with a convex class h1 d of positive solutions of the equation lu 0 in the present paper we give a probabilistic characterization of u1 d and a probabilistic representation of u u1 d in terms of a superdiffusion similar results are obtained also for a parabolic equation u lu u2

the baxter revolution i review the revolutionary impact rodney baxter has had on statistical mechanics beginning with his solution of the 8 vertex model in 1971 and the invention of corner transfer matrices in 1976 to the creation of the rsos models in 1984 and his continuing current work on the chiral potts model