correlation study of the athens stock exchange we study the year after year properties of three different portfolios traded in the athens stock exchange ase for the time period 1987 2004 we use the minimum spanning tree mst technique and the random matrix theory rmt which make it possible to examine at the same time the temporal evolution of the portfolios and of the market as a whole the first four moments of the distribution of correlations and the normalized tree lengths of the mst show a similar behaviour for all three portfolios however by studying topological properties of the mst such as the node degree k we are able to identify changes to the mst associated to each portfolio that are due to a crisis in the market like the one that happened during the period 1999 2001 we also see that while the effect of the market to the information content of the correlation matrix for all three portfolios is almost the same the market is affected differently by different economic sectors at different time periods r 2007 elsevier b v all rights reserved

localization of analytic regularity criteria on the vorticity and balance between the vorticity magnitude and coherence of the vorticity direction in the 3d nse the first part of the paper provides spatio temporal localization of a family of analytic regularity classes for the 3d nse obtained by beirao da veiga space time integrability of the gradient of the velocity on mathbb r 3 times 0 t which is out of the range of the sobolev embedding theorem reduction to the classical foias ladyzhenskaya prodi serrin space time integrability conditions on the velocity as well as the localization of the beale kato majda regularity criterion time integrability of the l norm of the vorticity the second part introduces a family of local scaling invariant hybrid geometric analytic classes in which coherence of the vorticity direction serves as a weight in the local spatio temporal integrability of the vorticity magnitude

a poincare inequality on loop spaces we show that the laplacian on the loop space over a class of riemannian manifolds has a spectral gap the laplacian is defined using the levi civita connection the brownian bridge measure and the standard bismut tangent spaces

random matrix theory and fund of funds portfolio optimisation abstract the proprietary nature of hedge fund investing means that it is common practise for managers to release minimal information about their returns the construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise in this paper random matrix theory rmt is applied to a cross correlation matrix c constructed using hedge fund returns data the analysis reveals a number of eigenvalues that deviate from the spectrum suggested by rmt the components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers the inverse participation ratio is used to quantify the number of components that participate in each eigenvector finally the correlation matrix is cleaned by separating the noisy part from the non noisy part of c this technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio leading to an improved risk profile for a fund of hedge funds

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

ornstein uhlenbeck processes with singular drifts integral estimates and girsanov densities we consider a perturbation of a hilbert space valued ornstein uhlenbeck process by a class of singular nonlinear non autonomous maximal monotone time dependent drifts the only further assumption on the drift is that it is bounded on balls in the hilbert space uniformly in time first we introduce a new notion of generalized solutions for such equations which we call pseudo weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation then we prove that their laws are absolutely continuous with respect to the law of the original ornstein uhlenbeck process in particular we show that pseudo weak solutions always have continuous sample paths in addition we obtain integrability estimates of the associated girsanov densities some of our results concern non random equations as well while probabilistic results are new even in finite dimensional autonomous settings

an extension and simpler proof of berselli cordoba s geometric regularity condition for the navier stokes system abstract in this short note we provide an simpler proof of berselli cordoba s geometric regularity condition for the navier stokes system moreover some interesting extensions are obtained

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

structure of a financial cross correlation matrix under attack abstract we investigate the structure of a perturbed stock market in terms of correlation matrices for the purpose of perturbing a stock market two distinct methods are used namely local and global perturbation the former involves replacing a correlation coefficient of the cross correlation matrix with one calculated from two gaussian distributed time series while the latter reconstructs the cross correlation matrix just after replacing the original return series with gaussian distributed time series concerning the local case it is a technical study only and there is no attempt to model reality the term global means the overall effect of the replacement on other untouched returns through statistical analyses such as random matrix theory rmt network theory and the correlation coefficient distributions we show that the global structure of a stock market is vulnerable to perturbation however apart from in the analysis of inverse participation ratios iprs the vulnerability becomes dull under a small scale perturbation this means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small scale perturbation in contrast when going down to the structure of business sectors we confirm that correlation based business sectors are regrouped in terms of iprs this result gives a clue about monitoring the effect of hidden intentions which are revealed via portfolios taken mostly by large investors

a strong regularity result for parabolic equations we consider a parabolic equation with a drift term u b u ut 0 under the condition divb 0 we prove that solutions possess dramatically better regularity than those provided by standard theory for example we prove continuity of solutions when not even boundedness is expected

pseudo paths towards minimum energy states in network dynamics abstract the dynamics of networks forming on heider balance theory moves towards lower tension states the condition derived from this theory enforces agents to reevaluate and modify their interactions to achieve equilibrium these possible changes in network s topology can be considered as various paths that guide systems to minimum energy states based on this theory the final destination of a system could reside on a local minimum energy jammed state or the global minimum energy balanced states the question we would like to address is whether jammed states just appear by chance or there exist some pseudo paths that bound a system towards a jammed state we introduce an indicator to suspect the location of a jammed state based on the inverse participation ratio method ipr we provide a margin before a local minimum where the number of possible paths dramatically drastically decreases this is a condition that proves adequate for ending up on a jammed states

the reaction of stock markets to crashes and events a comparison study between emerging and mature markets using wavelet transforms abstract we study here the behaviour of the first three eigenvalues 1 2 3 and their ratios 1 2 1 3 2 3 of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets it has been known for some time that the largest eigenvalue 1 contains information on the risk associated with the particular assets of which the covariance matrix is comprised here we wish to ascertain whether the subdominant eigenvalues 2 3 hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets to do this we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component our results appear to indicate that mature markets respond to crashes differently to emerging ones in that emerging markets may take up to two months to recover while major markets take less than a month to do so in addition the results appears to show that the subdominant eigenvalues 2 3 give additional information on market movement especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

on vorticity directions near singularities for the navier stokes flows with infinite energy we give a geometric nonblow up criterion on the direction of the vorticity for the three dimensional navier stokes flow whose initial data is just bounded and may have infinite energy we prove that under a restriction on behavior in time type i condition the solution does not blow up if the vorticity direction is uniformly continuous at the place where the vorticity magnitude is large this improves the regularity condition for the vorticity direction first introduced by p constantin and c fefferman 1993 for finite energy weak solution our method is based on a simple blow up argument which says that the situation looks like two dimensional under continuity of the vorticity direction we also discuss boundary value problems

space time localization of a class of geometric criteria for preventing blow up in the 3d nse a class of local in the space time conditions on the vorticity directions implying local regularity of weak solutions to the 3d navier stokes equations is established in all the preceding results the relevant geometric conditions although being local in nature have been assumed uniformly throughout the spatial regions of high vorticity magnitude and uniformly in time in addition similar results are obtained assuming a less restrictive integral condition on the vorticity directions

random matrix theory analysis of cross correlations in the us stock market evidence from pearson s correlation coefficient and detrended cross correlation coefficient abstract in this study we first build two empirical cross correlation matrices in the us stock market by two different methods namely the pearson s correlation coefficient and the detrended cross correlation coefficient dcca coefficient then combining the two matrices with the method of random matrix theory rmt we mainly investigate the statistical properties of cross correlations in the us stock market we choose the daily closing prices of 462 constituent stocks of s p 500 index as the research objects and select the sample data from january 3 2005 to august 31 2012 in the empirical analysis we examine the statistical properties of cross correlation coefficients the distribution of eigenvalues the distribution of eigenvector components and the inverse participation ratio from the two methods we find some new results of the cross correlations in the us stock market in our study which are different from the conclusions reached by previous studies the empirical cross correlation matrices constructed by the dcca coefficient show several interesting properties at different time scales in the us stock market which are useful to the risk management and optimal portfolio selection especially to the diversity of the asset portfolio it will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix r for the dcca coefficient because it does not obey the marcenko pastur distribution

levy gromov s isoperimetric inequality for an infinite dimensional diffusion generator we establish by simple semigroup arguments a levy gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the gaussian measure this produces in particular a new proof of the gaussian isoperimetric inequality this isoperimetric inequality strengthens the classical logarithmic sobolev inequality in this context a local version for the heat kernel measures is also proved which may then be extended into an isoperimetric inequality for the wiener measure on the paths of a riemannian manifold with bounded ricci curvature

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

dynamic topology and allometric scaling behavior on the vietnamese stock market abstract the impact of the vietnamese financial crisis during 2011 2012 into the stock market was revealed by a structural change of the minimum spanning tree mst constructed from the daily stock price we found that the mst has a star like structure during this period similar to that of the german market during the worldwide financial crisis of 2007 2008 m wiliski et al 2013 and a hierarchical scale free structure for the rest of time in addition we investigate the market from a complex network perspective by analyzing the allometric scaling behavior we found that all networks have the allometric scaling property with exponent ranging from 1 213 0 013 during the financial instability period to about 1 357 0 011 in normal time these values correspond to a complex dimension of the financial market of between 3 and 5 which need to be further investigated in the future

bilinear estimates in bmo and the navier stokes equations we prove that the bmo norm of the velocity and the vorticity controls the blow up phenomena of smooth solutions to the navier stokes equations our result is applied to the criterion on uniqueness and regularity of weak solutions in the marginal class

on the analysis of cross correlations in south african market data we report briefly on an application of random matrix theory to the analysis of sa financial market data an analysis of cross correlations in south african financial market data e print cond mat 0402389 correlation matrices c are constructed from 10 years of daily data for stocks listed on the johannesburg stock exchange from january 1993 to december 2002 spectral properties of c are tested against random matrix predictions we highlight some quantitative differences which arise when treating prices as existing only when measured as opposed to interpolating missing or illiquid trading days with a zero order hold

divergence theorems in path space abstract we obtain divergence theorems on the solution space of an elliptic stochastic differential equation defined on a smooth compact finite dimensional manifold m the resulting divergences are expressed in terms of the ricci curvature of m with respect to a natural metric on m induced by the stochastic differential equation the proofs of the main theorems are based on the lifting method of malliavin together with a fundamental idea of driver

hilbert schmidt groups as infinite dimensional lie groups and their riemannian geometry abstract we describe the exponential map from an infinite dimensional lie algebra to an infinite dimensional group of operators on a hilbert space notions of differential geometry are introduced for these groups in particular the ricci curvature which is understood as the limit of the ricci curvature of finite dimensional groups is calculated we show that for some of these groups the ricci curvature is

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

localization and geometric depletion of vortex stretching in the 3d nse vortex stretching and consequently the evolution of the vorticity is localized on an arbitrarily small space time cylinder this yields a complete localization of the geometric condition s for the regularity involving coherence of the vorticity direction in particular it implies the regularity of any geometrically constrained leray solution independently of the type of the spatial domain or the boundary conditions

logarithmic sobolev inequalities for pinned loop groups abstract letgbe a connected compact type lie group equipped with anadg invariant inner product on the lie algebra g ofg given this data there is a well known left invariant h1 riemannian structure on l l g the infinite dimensional group of continuous based loops ing using this riemannian structure we define and construct a heat kernel t g0 associated to the laplace beltrami operator on l g heret 0 g0 l g and t g0 is a certain probability measure on l g for fixedg0 l g andt 0 we use the measure t g0 and the riemannian structure on l g to construct a classical pre dirichlet form the main theorem of this paper asserts that this pre dirichlet form admits a logarithmic sobolev inequality

blow up rate estimates for weak solutions of the navier stokes equations the interior regularity problem for the leray weak solutions u of the navier stokes equations in a domain rn with n 3 is investigated it is shown that u is regular in a neighbourhood of a point x t omega 0 t if there exist constants 0 1 and small 0 such that with q 1 k i x t x r n x x 1 k t 1 k 2 t 1 k 2 if x t is an irregular point of u there exists a sequence of non zero measure sets e ki q 1 ki x t for i 1 2 such that the blow up rate estimate holds

precise asymptotics of certain wiener functionals abstract in this article we present a method for developing certain wiener integrals in an asymptotic expansion as the variance of the wiener goes to 0 the basic ideas are a combination of methods borrowed from the theory of large deviations together with techniques from the calculus of wiener space

on estimation of the logarithmic sobolev constant and gradient estimates of heat semigroups this paper presents some explicit lower bound estimates of logarithmic sobolev constant for diffusion processes on a compact riemannian manifold with negative ricci curvature let ric k for some k 0 and d d be respectively the dimension and the diameter of the manifold if the boundary of the manifold is either empty or convex then the logarithmic sobolev constant for brownian motion is not less than

square integrable holomorphic functions on infinite dimensional heisenberg type groups we introduce a class of non commutative complex infinite dimensional heisenberg like lie groups based on an abstract wiener space the holomorphic functions which are also square integrable with respect to a heat kernel measure on these groups are studied in particular we establish a unitary equivalence between the square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the lie algebra of this class of groups using quasi invariance of the heat kernel measure we also construct a skeleton map which characterizes globally defined functions from the l 2 closure of holomorphic polynomials by their values on the cameron martin subgroup

on depletion of the vortex stretching term in the 3d navier stokes equations certain new cancellation properties in the vortex stretching term are detected leading to new geometric criteria for preventing finite time blow up in the 3d navier stokes equations

integration by parts and quasi invariance for heat kernel measures on loop groups abstract integration by parts formulas are established both for wiener measure on the path space of a loop group and for the heat kernel measures on the loop group the wiener measure is defined to be the law of a certain loop group valued brownian motion and the heat kernel measures are time t t 0 distributions of this brownian motion a corollary of either of these integrations by parts formulas is the closability of the pre dirichlet form considered by b k driver and t lohrenz 1996 j functional anal 140 381 448 we also show that the heat kernel measures are quasi invariant under right under right and left translations by finite energy loops

navier stokes equations and area of interfaces we present new a priori estimates for the vorticity of solutions of the three dimensional navier stokes equations these estimates imply that thel 1 norm of the vorticity is a priori bounded in time and that the time average of the 4 3 e power of thel 4 3 e spatial norm of the gradient of the vorticity is a priori bounded using these bounds we construct global leray weak solutions of the navier stokes equations which satisfy these inequalities in particular it follows that vortex sheet vortex line and even more general vortex structures with arbitrarily large vortex strengths are initial data which give rise to global weak solutions of this type of the navier stokes equations next we apply these inequalities in conjunction with geometric measure theoretical arguments to study the two dimensional hausdorff measure of level sets of the vorticity magnitude we obtain a priori bounds on an average such measure when expressed in terms of the reynolds number and the kolmogorov dissipation length these bounds are left langle mu right rangle leqq frac l 3 eta left 1 operatorname re 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 the right hand side of this inequality has a simple geometrical interpretation it represents the area of a union of non overlapping spheres of radii which fill a fraction of the spatial domain as the reynolds number increases this fraction decreases we study also the area of level sets of scalars and in particular isotherms in rayleigh benard convection we define a quantity r t x 0 describing an average value of the area of a portion of a level set contained in a small ball of radiusr about the pointx 0 we obtain the inequality left langle mu right rangle r t left x 0 right leqq c kappa 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 r 5 mathord left vphantom 5 2 right kern nulldelimiterspace 2 left langle v left x 0 right right rangle 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 wherek is the diffusivity constant and is the velocity the inequality is valid forr small but larger than a small scale k 1 in the case of turbulent velocities this scale is smaller than the smallest significant physical scale suggesting that 2 5 is a lower bound for the fractal dimension of an ensemble average interface in turbulent flow a fact which agrees with the experimental lower bound of 2 35 we define a similar quantity t representing an average value of the area of a portion of a level set contained in the region of spaced x d dist x d whered is the domain of aspect ratio of order one and diameterl where the convection takes place we obtain the inequality left langle mu right rangle delta t leqq c left l 3 delta 1 l 5 mathord left vphantom 5 2 right kern nulldelimiterspace 2 delta 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 ra 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right where ra is the rayleigh number

quasi invariance of brownian measures on the group of circle homeomorphisms and infinite dimensional riemannian geometry abstract a cameron martin type theorem is proved for the canonical brownian motion on the group of homeomorphisms of the circle

heat kernel analysis and cameron martin subgroup for infinite dimensional groups abstract the heat kernel measure t is constructed on gl h the group of invertible operators on a complex hilbert space h this measure is determined by an infinite dimensional lie algebra g and a hermitian inner product on it the cameron martin subgroup g cm is defined and its properties are discussed in particular there is an isometry from the l 2 t closure of holomorphic polynomials into a space h t g cm of functions holomorphic on g cm this means that any element from this l 2 t closure of holomorphic polynomials has a version holomorphic on g cm in addition there is an isometry from h t g cm into a hilbert space associated with the tensor algebra over g the latter isometry is an infinite dimensional analog of the taylor expansion as examples we discuss a complex orthogonal group and a complex symplectic group

heat kernel analysis on infinite dimensional heisenberg groups abstract we introduce a class of non commutative heisenberg like infinite dimensional lie groups based on an abstract wiener space the ricci curvature tensor for these groups is computed and shown to be bounded brownian motion and the corresponding heat kernel measures t t 0 are also studied we show that these heat kernel measures admit 1 gaussian like upper bounds 2 cameron martin type quasi invariance results 3 good l p bounds on the corresponding radon nikodym derivatives 4 integration by parts formulas and 5 logarithmic sobolev inequalities the last three results heavily rely on the boundedness of the ricci tensor

brownian measures on jordan virasoro curves associated to the weil petersson metric abstract in this paper existence of the brownian measure on jordan curves with respect to the weil petersson metric is established the step from brownian motion on the diffeomorphism group of the circle to brownian motion on jordan curves in c requires probabilistic arguments well beyond the classical theory of conformal welding due to the lacking quasi symmetry of canonical brownian motion on diff s 1 a new key step in our construction is the systematic use of a kahlerian diffusion on the space of jordan curves for which the welding functional gives rise to conformal martingales together with a douady earle type conformal extension of vector fields on the circle to the disk

smoothness of heat kernel measures on infinite dimensional heisenberg like groups abstract we study measures associated to brownian motions on infinite dimensional heisenberg like groups in particular we prove that the associated path space measure and heat kernel measure satisfy a strong definition of smoothness

comparing the structure of an emerging market with a mature one under global perturbation a b s t r a c t in this paper we investigate the tehran stock exchange tse and dow jones industrial average djia in terms of perturbed correlation matrices to perturb a stock market there are two methods namely local and global perturbation in the local method we replace a correlation coefficient of the cross correlation matrix with one calculated from two gaussian distributed time series whereas in the global method we reconstruct the correlation matrix after replacing the original return series with gaussian distributed time series the local perturbation is just a technical study we analyze these markets through two statistical approaches random matrix theory rmt and the correlation coefficient distribution by using rmt we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks we find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with gaussian distributed time series the mean values of correlation coefficients the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the rmt prediction fall sharply in both markets by comparing these two markets we can see that the djia is more sensitive to global perturbations these findings are crucial for risk management and portfolio selection

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence

time dependent cross correlations between different stock returns a directed network of influence we study the time dependent cross correlations of stock returns i e we measure the correlation as the function of the time shift between pairs of stock return time series using tick by tick data we find a weak but significant effect showing that in many cases the maximum correlation appears at nonzero time shift indicating directions of influence between the companies due to the weakness of this effect and the shortness of the characteristic time of the order of a few minutes our findings are compatible with market efficiency the interaction of companies defines a directed network of influence

measures of uncertainty in market network analysis abstract a general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed two measures of statistical uncertainty are introduced and discussed one is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors it is shown that for some important cases the second measure is a particular case of the first one the proposed approach is illustrated by numerical evaluation of statistical uncertainty for popular network structures minimum spanning tree planar maximally filtered graph market graph maximum cliques and maximum independent sets in the framework of gaussian network model of stock market

network trending leadership followership and neutrality among companies a random matrix approach abstract in this article we analyze the cross correlation between returns of different stocks to answer the following important questions the first one is if there exists collective behavior in a financial market how could we detect it and the second question is is there a particular company among the companies of a market as the leader of the collective behavior or is there no specified leadership governing the system similar to some complex systems we use the method of random matrix theory to answer the mentioned questions cross correlation matrix of index returns of four different markets is analyzed the participation ratio quantity related to each matrices eigenvectors and the eigenvalue spectrum is calculated we introduce shuffled matrix created of cross correlation matrix in such a way that the elements of the later one are displaced randomly comparing the participation ratio quantities obtained from a correlation matrix of a market and its related shuffled one on the bulk distribution region of the eigenvalues we detect a meaningful deviation between the mentioned quantities indicating the collective behavior of the companies forming the market by calculating the relative deviation of participation ratios we obtain a measure to compare the markets according to their collective behavior answering the second question we show there are three groups of companies the first group having higher impact on the market trend called leaders the second group is followers and the third one is the companies who have not a considerable role in the trend the results can be utilized in portfolio construction