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作者：Borodin, Alexei; Bufetov, Alexey
作者单位：Massachusetts Institute of Technology (MIT); University of Bonn; University of Bonn
摘要：We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir-AngelValko and Borodin-Wheeler. We are also able to use the symmetry, together with previously known results for uncolored model...
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作者：Gamarnik, David; Jagannath, Aukosh
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of Waterloo
摘要：We consider the algorithmic problem of finding a near ground state (near optimal solution) of a p-spin model. We show that for a class of algorithms broadly defined as Approximate Message Passing (AMP), the presence of the Overlap Gap Property (OGP), appropriately defined, is a barrier. We conjecture that, when p >= 4, the model does indeed exhibit OGP (and prove it for the space of binary solutions). Assuming the validity of this conjecture, as an implication the AMP fails to find near ground...
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作者：Gwynne, Ewain; Pfeffer, Joshua
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Let M be the infinite spanning-tree-weighted random planar map, which is the local limit of finite random planar maps sampled with probability proportional to the number of spanning trees they admit. We show that a.s. the M-graph-distance diameter of the external diffusion-limited aggregation (DLA) cluster on M run for m steps is of order m(2/d+om(1)), where d is the metric ball volume growth exponent for M (which was shown to exist by Ding and Gwynne (Comm. Math. Phys. 374 (2020) 1877-1934). ...
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作者：Bhamidi, Shankar; Nam, Danny; Oanh Nguyen; Sly, Allan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Princeton University
摘要：In this paper we establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short survival). We prove that the survival threshold lambda(1) for a Galton-Watson tree is strictly positive if and only if its offspring distribution xi has an exponential tail, that is, Ee(c xi) < infinity for some c > 0, settling a conjecture by Huang and Durrett (2018). On the random graph with degree distributio...
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作者：Holden, Nina; Peres, Yuval; Zhai, Alex
作者单位：Massachusetts Institute of Technology (MIT); Microsoft; Stanford University
摘要：Given a collection L of n points on a sphere S-n(2) of surface area n, a fair allocation is a partition of the sphere into n cells each of area 1, and each associated with a distinct point of L. We show that if the n points are chosen uniformly at random and the partition is defined by considering a gravitational potential defined by the n points, then the expected distance between a point on the sphere and the associated point of L is O (root log n) which is optimal by a result of Ajtai, Koml...
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作者：Johansson, Kurt; Lambert, Gaultier
作者单位：Royal Institute of Technology; University of Zurich
摘要：In this article we obtain a superexponential rate of convergence in total variation between the traces of the first m powers of a n x n random unitary matrices and a 2m-dimensional Gaussian random variable. This generalizes previous results in the scalar case to the multivariate setting, and we also give the precise dependence on the dimensions m and n in the estimates with explicit constants. We are especially interested in the regime where m grows with n and our main result basically states ...
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作者：Beckman, Erin; Cook, Keisha; Eikmeier, Nicole; Hernandez-Torres, Sarai; Junge, Matthew
作者单位：Concordia University - Canada; Tulane University; Grinnell College; Technion Israel Institute of Technology; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the variant in which red particles die and describe the phase diagram for the resulting process on infinite d-ary trees. A novel connection to weighted Catalan numbers makes it possible to characterize the critical behavior.
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作者：Krylov, N., V
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For the Ito stochastic equations in R-d with drift in L-d, several results are discussed, such as the existence of weak solutions, the existence of the corresponding Markov process, the Aleksandrov type estimates of their Green's functions, which yield their summability to the power of d/(d - 1), the Fabes-Stroock type estimates, which show that Green's functions are summable to a higher degree, the Fanghua Lin type estimates, which are one of the main tools in the W-p(2)-theory of fully nonli...
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作者：Forman, Noah; Pal, Soumik; Rizzolo, Douglas; Winkel, Matthias
作者单位：McMaster University; University of Washington; University of Washington Seattle; University of Delaware; University of Oxford
摘要：We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters (a, 0) and (a, a). The construction has two steps. The first is a general construction of interval partition processes obtained previously by decorating the jumps of a Levy process with independent excursions. Here, we focus on the second step which requires explicit transition kernels and, what we call, pseudostationarity. This allows us to study p...
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作者：Dimitrov, Evgeni; Matetski, Konstantin
作者单位：Columbia University
摘要：In this paper we show that a Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its top curve, that is, the finite-dimensional sets of the top curve form a separating class. A particular consequence of our result is that the parabolic Airy line ensemble is the unique Brownian Gibbsian line ensemble, whose top curve is the parabolic Airy(2) process.
