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作者：Bertini, Lorenzo; Giacomin, Giambattista; Poquet, Christophe
作者单位：Sapienza University Rome; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
摘要：We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition at a critical value of the interaction strength parameter K, in the limit of the number N of rotators going to infinity. A Fokker-Planck PDE captures the evolution of the empirical measure of the system as N ->infinity, at least for finite times and when the empirical measure of the system at time...
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作者：Burdzy, Krzysztof; Scheutzow, Michael
作者单位：University of Washington; University of Washington Seattle; Technical University of Berlin
摘要：We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at . We show that these processes do not have to have the distribution of standard Brownian motion in the backward direction of time, no matter which random time we take as the origin. We study the maximum and minimum rates of growth for these processes in the backward direction. We also address the question of which ext...
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作者：Burdzy, Krzysztof; Nualart, David; Swanson, Jason
作者单位：University of Washington; University of Washington Seattle; University of Kansas; State University System of Florida; University of Central Florida
摘要：The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter . We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.
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作者：Bourgade, Paul; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point away from the unit circle. More precisely, if for arbitrarily small , the circular law is valid around up to scale for any under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.
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作者：Maida, Mylene; Maurel-Segala, Edouard
作者单位：Universite Paris Saclay
摘要：Talagrand's inequalities provide a link between two fundamentals concepts of probability: transportation and entropy. The study of the counterpart of these inequalities in the context of free probability has been initiated by Biane and Voiculescu and later extended by Hiai, Petz and Ueda for convex potentials. In this work, we prove a free analogue of a result of Bobkov and Gotze in the classical setting, thus providing free transport-entropy inequalities for a very natural class of measures a...
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作者：Dalalyan, Arnak; Ingster, Yuri; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Saint Petersburg State Electrotechnical University
摘要：We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. The compound model is characterized by three main parameters: the structure parameter describing the macroscopic form of the compound function, the microscopic sparsity parameter indicating the maximal number of relevant covariates in each compon...
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作者：Mossel, Elchanan; Sly, Allan; Tamuz, Omer
作者单位：Weizmann Institute of Science; University of California System; University of California Berkeley
摘要：We study a standard model of economic agents on the nodes of a social network graph who learn a binary state of the world , from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs with if with probability tending to as all agents in eventually estimate correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.
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作者：Dolera, Emanuele; Regazzini, Eugenio
作者单位：Universita di Modena e Reggio Emilia; University of Pavia; Consiglio Nazionale delle Ricerche (CNR); Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes (IMATI-CNR)
摘要：The present work provides a definitive answer to the problem of quantifying relaxation to equilibrium of the solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules. Under really mild conditions on the initial datum and a weak, physically consistent, angular cutoff hypothesis, our main result (Theorem 1) contains the first precise statement that the total variation distance between the solution and the limiting Maxwellian distribution admits an upper bound of the form...
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作者：Dolinsky, Yan; Soner, H. Mete
作者单位：Hebrew University of Jerusalem; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI)
摘要：The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fi...
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作者：Abraham, Romain; Delmas, Jean-Francois; Hoscheit, Patrick
作者单位：Universite de Orleans; Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on L,vy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height, using a spinal decomposition of the tree, similar to the clas...
