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作者：Bella, Peter; Schaeffner, Mathias
作者单位：Dortmund University of Technology
摘要：We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on Z(d). In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.
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作者：Petrov, Leonid; Saenz, Axel
作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia; University of Warwick
摘要：We obtain a new relation between the distributions mu(t) at different times t >= 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions mu(t) backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammers...
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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 consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motion perturbed at its extrema (BMPE). All parameters of the limiting process are given explicitly in terms of those of the cookie Markov chain at a single site. While our results extend the results in Dolgopyat and Kosygina (Electron Commun Prob...
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作者：Driver, Bruce K.; Hall, Brian; Kemp, Todd
作者单位：University of California System; University of California San Diego; University of Notre Dame
摘要：The free multiplicative Brownian motion b(t) is the large-N limit of the Brownian motion on GL(N; C), in the sense of (*)-distributions. The natural candidate for the large-N limit of the empirical distribution of eigenvalues is thus the Brown measure of b(t). In previous work, the second and third authors showed that this Brown measure is supported in the closure of a region Sigma(t) that appeared in the work of Biane. In the present paper, we compute the Brown measure completely. It has a co...
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作者：Yang, Kevin
作者单位：Stanford University
摘要：This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP from Corwin and Shen (Commun Pure Appl Math 71(10):2065-2128, 2018), Parekh (Commun Math Phys 365:569-649, 2019. https://doi.org/10.1007/s00220-018-3258-x) . but admitting non-simple interactions both at the boundary and within the bulk of the particle system....
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作者：Nestoridi, Evita; Olesker-Taylor, Sam
作者单位：Princeton University; University of Cambridge
摘要：In a recent breakthrough, Teyssier (Ann Probab 48(5):2323-2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to s...
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作者：Liu, Jingbo
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We give a complete solution to an open problem of Thomas Cover in 1987 about the capacity of a relay channel in the general discrete memoryless setting without any additional assumptions. The key step in our approach is to lower bound a certain soft-max of a stochastic process by convex geometry methods, which is based on two ideas: First, the soft-max is lower bounded in terms of the supremum of another process, by approximating a convex set with a polytope with bounded number of vertices. Se...
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作者：Galashin, Pavel
作者单位：University of California System; University of California Los Angeles
摘要：Given a finite rhombus tiling of a polygonal region in the plane, the associated critical Z-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between boundary vertices in terms of the shape of the region. When the region is a regular polygon, our formula becomes an explicit trigonometric sum.
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作者：Della Maestra, Laetitia; Hoffmann, Marc
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a system of N interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time horizon, we investigate nonparametric estimation of the solution of the associated nonlinear Fokker-Planck equation, together with the drift term that controls the interactions, in a large population limit N -> infinity. We build data-driven kernel estimators a...
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作者：Lammers, Piet
作者单位：Universite Paris Saclay
摘要：The interest is in models of integer-valued height functions on shift-invariant planar graphs whose maximum degree is three. We prove delocalisation for models induced by convex nearest-neighbour potentials, under the condition that each potential function is an excited potential, that is, a convex symmetric potential function V with the property that V(+/- 1) <= V(0) + log 2. Examples of such models include the discrete Gaussian and solid-on-solid models at inverse temperature beta <= log 2, ...
