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作者：Chong, Carsten; Kevei, Peter
作者单位：Columbia University; Szeged University
摘要：We show that the spatial profile of the solution to the stochastic heat equation features multiple layers of intermittency islands if the driving noise is non-Gaussian. On the one hand, as expected, if the noise is sufficiently heavy-tailed, the largest peaks of the solution will be taller under multiplica-tive than under additive noise. On the other hand, surprisingly, as soon as the noise has a finite moment of order d2, where dis the spatial dimension, the largest peaks will be of the same ...
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作者：Diaconu, Simona
作者单位：Stanford University
摘要：The Tracy-Widom distributions are among the most famous laws in probability theory, partly due to their connection with Wigner matrices. In particular, for A = 1/root n(a(ij))(1 <= i,j <= n) is an element of R-nxn symmetric with (a(ij))(1 <= i <= j <= n) i.i.d. standard normal, the fluctuations of its largest eigenvalue lambda(1)(A) are asymptotically described by a real-valued Tracy-Widom distribution TW1 : n(2/3)(lambda(1)(A) - 2) double right arrow TW1. As it often happens, Gaussianity can ...
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作者：Kosygina, Elena; Mountford, Thomas; Peterson, Jonathon
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
摘要：We use generalized Ray-Knight theorems, introduced by B. Toth in 1996, together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusively scaled self-interacting random walks (SIRW) to Brownian motions perturbed at extrema (BMPE). Toth's work studied two classes of SIRWs: asymptotically free and polynomially self-repelling walks. For both classes Toth has shown, in particular, that the d...
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作者：Sjostrand, Jonas
作者单位：Malardalen University
摘要：A locally uniform random permutation is generated by sampling n points independently from some absolutely continuous distribution p on the plane and interpreting them as a permutation by the rule that i maps to j if the ith point from the left is the jth point from below. As n tends to infinity, decreas-ing subsequences in the permutation will appear as curves in the plane, and by interpreting these as level curves, a union of decreasing subsequences give rise to a surface. We show that, under...
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作者：Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider the exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the pro-cess, in terms of certain simple spectral statistics of the underlying network. Among other consequences we establish a nonconservative analogue of Al-dous's spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary d...
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作者：Brito, Gerandy; Damron, Michael; Hanson, Jack
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY)
摘要：In first-passage percolation (FPP), one places nonnegative random vari-ables (weights) (te) on the edges of a graph and studies the induced weighted graph metric. We consider FPP on Zd for d > 2 and analyze the geometric properties of geodesics, which are optimizing paths for the metric. Specifi-cally, we address the question of existence of bigeodesics, which are doubly-infinite paths whose subpaths are geodesics. It is a famous conjecture origi-nating from a question of Furstenberg and most ...
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作者：Contat, Alice; Curien, Nicolas
作者单位：Universite Paris Saclay
摘要：Consider a uniform rooted Cayley tree T-n with n vertices and let m cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives towards the root of the tree and parks as soon as possible. Lackner and Panholzer (J. Combin. Theory Ser. A 142 (2016) 1-28) established a phase transition for this process when m approximate to n/2. In this work, we couple this model with a variant of the classical ...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W12+epsilon,loc, and the drift in a Morrey class containing Ld. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.
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作者：Cerf, Raphael; Dembin, Barbara
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the standard model of i.i.d. first passage percolation on Z(d) given a distribution G on [0, +infinity] (-infinity is allowed). When G([0, +infinity)) > p(c) (d), it is known that the time constant mu(G) exists. We are interested in the regularity properties of the map G bar right arrow mu(G). We first study the specific case of distributions of the form G(p) = p delta(1) + (1 - p)delta(infinity) for p > p(c) (d). In this case, the travel time between two points is equal to the len...
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作者：Chasapsis, Giorgos; Nayar, Piotr; Tkocz, Tomasz
作者单位：Carnegie Mellon University; University of Warsaw
摘要：We show that the two-dimensional minimum-volume central section of the n-dimensional cross-polytope is attained by the regular 2n-gon. We estab-lish stability-type results for hyperplane sections of l(p)-balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, ex-ploring connections between negative moments of projections of random vec-tors uniformly distributed on convex bodies and volume of their sections.
