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作者：Kulik, Alexei; Scheutzow, Michael
作者单位：Wroclaw University of Science & Technology; Technical University of Berlin
摘要：We develop a new generalized coupling approach to the study of stochastic delay equations with Holder continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak solutions, and establish weak ergodic rates for the corresponding segment processes. We also prove, under additional smoothness assumptions on the coefficients, stabilization rates for the sensitivities in the initial value of the corresponding semigroups.
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作者：Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; New York University; NYU Shanghai; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.
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作者：Cerny, Jiri; Drewitz, Alexander
作者单位：University of Basel; University of Cologne
摘要：We consider branching random walk in spatial random branching environment (BRWRE) in dimension one, as well as related differential equations: the Fisher-KPP equation with random branching and its linearized version, the parabolic Anderson model (PAM). When the random environment is bounded, we show that after recentering and scaling, the position of the maximal particle of the BRWRE, the front of the solution of the PAM, as well as the front of the solution of the randomized Fisher-KPP equati...
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作者：Ben Arous, Gerard; Gheissari, Reza; Jagannath, Aukosh
作者单位：New York University; University of Waterloo
摘要：We study the algorithmic thresholds for principal component analysis of Gaussian k-tensors with a planted rank-one spike, via Langevin dynamics and gradient descent. In order to efficiently recover the spike from natural initializations, the signal-to-noise ratio must diverge in the dimension. Our proof shows that the mechanism for the success/failure of recovery is the strength of the curvature of the spike on the maximum entropy region of the initial data. To demonstrate this, we study the d...
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作者：Duminil-Copin, Hugo; Ganguly, Shirshendu; Hammond, Alan; Manolescu, Ioan
作者单位：Universite Paris Saclay; University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of Fribourg
摘要：Let c(n) = c(n)(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice Z(d). Let mu, = lim(n) c(n)(1/n) denote the connective constant of Z(d). In 1962, Hammersley and Welsh (Quart. J. Math. Oxford Ser (2) 13 (1962) 108-110) proved that, for each d >= 2, there exists a constant C > 0 such that c(n) <= exp(C-n(1/2))mu(n) for all n is an element of N. While it is anticipated that c(n)mu(-n). has a power-law growth in n, the best-...
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作者：Schmidt, Marius A.
作者单位：University of Basel
摘要：We give a simple proof of the theorem by Dembo, Peres, Rosen and Zeitouni (DPRZ) regarding the time Brownian motion needs to cover every epsilon ball on the two-dimensional unit torus in the epsilon SE arrow 0 limit.
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作者：Beliaev, Dmitry; Muirhead, Stephen; Rivera, Alejandro
作者单位：University of Oxford; University of London; Queen Mary University London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii) events measurable with respect to the number of connected components of level or excursion sets of a given diffeomorphism class and (iii) persistence events. As an application of the covariance formula, we derive strong mixing bounds for to...
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作者：Landon, Benjamin; Lopatto, Patrick; Marcinek, Jake
作者单位：Massachusetts Institute of Technology (MIT); Harvard University
摘要：We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalized Wigner ensembles, provided that the first four moments of their matrix entries match. As an application, we extend results of Ben Arous-Bourgade and Feng-Wei that identify the limit of the maximal eigenvalue gap in the bulk of the GUE to all complex Hermitian generalized Wigner matrices.
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作者：Holroyd, Alexander E.; Hutchcroft, Tom; Levy, Avi
作者单位：University of Washington; University of Washington Seattle; University of Cambridge; Microsoft
摘要：We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence st...
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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of Cambridge; Universite Paris Cite
摘要：We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing time from any initial configuration, and establish the cutoff phenomenon. The intuitive picture is that the system separates into a slowly evolving solid phase and a quickly relaxing liquid phase: as time passes, the solid phase dissolves into the liquid phas...
