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作者：Bauerschmidt, Roland; Huang, Jiaoyang; Knowles, Antti; Yau, Horng-Tzer
作者单位：University of Cambridge; Harvard University; University of Geneva
摘要：We consider the uniform random d-regular graph on N vertices, with d is an element of [N-alpha, N2/3-alpha] for arbitrary alpha > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.
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作者：Cheridito, Patrick; Nam, Kihun
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be translated into a fixed-point problem in a space of random vectors. This makes it possible to employ general fixed-point arguments to establish the existence of a solution. For instance, Banach's contraction mapping theorem can be used to derive general existence...
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作者：Addario-Berry, Louigi; Penington, Sarah
作者单位：McGill University; University of Oxford
摘要：We augment standard branching Brownian motion by adding a competitive interaction between nearby particles. Informally, when particles are in competition, the local resources are insufficient to cover the energetic cost of motion, so the particles' masses decay. In standard BBM, we may define the front displacement at time t as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the loc...
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作者：Lubetzky, Eyal; Sly, Allan
作者单位：New York University; University of California System; University of California Berkeley
摘要：On any locally-finite geometry, the stochastic Ising model is known to be contractive when the inverse-temperature beta is small enough, via classical results of Dobrushin and of Holley in the 1970s. By a general principle proposed by Peres, the dynamics is then expected to exhibit cutoff. However, so far cutoff for the Ising model has been confirmed mainly for lattices, heavily relying on amenability and log Sobolev inequalities. Without these, cutoff was unknown at any fixed beta > 0, no mat...
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作者：Sabot, Christophe; Tarres, Pierre; Zeng, Xiaolin
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); New York University; NYU Shanghai; Tel Aviv University; Universite PSL; Universite Paris-Dauphine; New York University; NYU Shanghai
摘要：We introduce a new exponential family of probability distributions, which can be viewed as a multivariate generalization of the inverse Gaussian distribution. Considered as the potential of a random Schrodinger operator, this exponential family is related to the random field that gives the mixing measure of the Vertex Reinforced Jump Process (VRJP), and hence to the mixing measure of the Edge Reinforced Random Walk (ERRW), the so-called magic formula. In particular, it yields by direct computa...
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作者：Belinschi, Serban T.; Bercovici, Hari; Capitaine, Mireille; Fevrier, Maxime
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Queens University - Canada; Romanian Academy; University of Bucharest; Institute of Mathematics of the Romanian Academy; Indiana University System; Indiana University Bloomington; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We characterize the possible outliers in the spectrum of large deformed unitarily invariant additive and multiplicative models, as well as the eigenvectors corresponding to them. We allow both the nondeformed unitarily invariant model and the perturbation matrix to have nontrivial limiting eigenvalue distributions and spiked outliers in their spectrum. The free subordination functions play a key role in this analysis.
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作者：Benaych-Georges, Florent
作者单位：Universite Paris Cite
摘要：The single ring theorem, by Guionnet, Krishnapur and Zeitouni in Ann. of Math. (2) 174 (2011) 1189-1217, describes the empirical eigenvalue distribution of a large generic matrix with prescribed singular values, that is, an N x N matrix of the form A = UTV, with U, V some independent Haardistributed unitary matrices and T a deterministic matrix whose singular values are the ones prescribed. In this text, we give a local version of this result, proving that it remains true at the microscopic sc...
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作者：Kyprianou, Andreas E.; Pagett, Steven W.; Rogers, Tim; Schweinsberg, Jason
作者单位：University of Bath; University of California System; University of California San Diego
摘要：An important property of Kingman's coalescent is that, starting from a state with an infinite number of blocks, over any positive time horizon, it transitions into an almost surely finite number of blocks. This is known as coming down from infinity. Moreover, of the many different (exchangeable) stochastic coalescent models, Kingman's coalescent is the fastest to come down from infinity. In this article, we study what happens when we counteract this fastest coalescent with the action of an ext...
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作者：Khare, Apoorva; Rajaratnam, Bala
作者单位：Stanford University; University of California System; University of California Davis; University of Sydney; Indian Institute of Science (IISC) - Bangalore
摘要：We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989) 789-808], Klass and Nowicki [Ann. Probab. 28 (2000) 851-862], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001) 447-466]. Finally, we show that the Hoffmann...
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作者：Letizia, Viviana; Olla, Stefano
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We consider a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a time-varying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive space-time rescaling the volume strain distribution of the chain evolves following a nonlinear diffusive equation. The stationary states of the dynamics are of nonequilibrium and have a positive entropy production, so the classical relative entropy methods cannot be us...
