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作者：Matetski, Konstantin; Remenik, Daniel
作者单位：Columbia University; Universidad de Chile; Universidad de Chile
摘要：The explicit biorthogonalization method, developed in [24] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several interacting particle systems in the KPZ universality class. The method is applied to sequential and parallel update versions of each of the four variants of discrete time TASEP (with Bernoulli and geometric jumps, and with block and push dynamics) which have determinantal transition probabilities; to continuous t...
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作者：Mao, Cheng; Rudelson, Mark; Tikhomirov, Konstantin
作者单位：University System of Georgia; Georgia Institute of Technology; University of Michigan System; University of Michigan
摘要：This paper deals with the problem of graph matching or network alignment for Erdos- Renyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let G and G' be G(n, p) Erdos-Renyi graphs marginally, identified with their adjacency matrices. Assume that G and G' are correlated such that E[G(ij)G'(ij)] = p(1 - alpha). For a permutation pi representing a latent matching between the vertices of G and G', denote by G(pi) the graph obtained from permuting the ...
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作者：Dauvergne, Duncan
作者单位：University of Toronto
摘要：Consider the restriction of the directed landscape L(x, s; y, t) to a set of the form {x(1), . . . , x(k)} x {s(0)} x R x {t(0)}. We show that on any such set, the directed landscape is given by a last passage problem across k locally Brownian functions. The k functions in this last passage isometry are built from certain marginals of the extended directed landscape. As applications of this construction, we show that the Airy difference profile is locally absolutely continuous with respect to ...
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作者：Galeati, Lucio; Harang, Fabian A.; Mayorcas, Avi
作者单位：University of Bonn; University of Oslo; BI Norwegian Business School; University of Cambridge
摘要：We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter H is an element of (0, 1). We establish strong well-posedness under a variety of assumptions on the drift; these include the choice B(., mu) = (f * mu)(.) + g(.), f, g is an element of B-infinity,infinity(alpha), alpha > 1 - 1/2H, thus extending the results by Catellier and Gubinelli (Stochast Process Appl 126(8):23...
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作者：Ganguly, Shirshendu; Hegde, Milind
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We consider last passage percolation on Z(2) with general weight distributions, which is expected to be a member of the Kardar-Parisi-Zhang (KPZ) universality class. In this model, an oriented path between given endpoints which maximizes the sum of the i.i.d. weight variables associated to its vertices is called a geodesic. Under natural conditions of curvature of the limiting geodesic weight profile and stretched exponential decay of both tails of the point-to-point weight, we use geometric a...
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作者：Andreis, Luisa; Koenig, Wolfgang; Langhammer, Heide; Patterson, Robert I. A.
作者单位：Polytechnic University of Milan; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We study an inhomogeneous sparse random graph, G(N), on [N] = {1, . . . , N} as introduced in a seminal paper by Bollobas et al. (Random Struct Algorithms 31(1):3-122, 2007): vertices have a type (here in a compact metric space S), and edges between different vertices occur randomly and independently over all vertex pairs, with a probability depending on the two vertex types. In the limit N -> infinity, we consider the sparse regime, where the average degree is O (1). We prove a large-deviatio...
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作者：Cooperman, William
作者单位：University of Chicago
摘要：We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet-Souganidis, who proved qualitative homogenization in a more general ergodic environment.
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作者：Auffinger, Antonio; Gorski, Christian
作者单位：Northwestern University
摘要：We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini and Tessera (Electron J Probab 20:1-20, 2015) and Cantrell and Furman (Groups Geom Dyn 11(4):1307-1345, 2017) show that scaling limits of such FPP are given by Carnot-Caratheodory metrics on the associated graded nilpotent Lie group. We show a converse, i.e. that for any Cayley graph of a finitely generated nilpotent group, any Car...
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作者：Tikhomirov, Konstantin; Youssef, Pierre
摘要：Consider the switch chain on the set of d-regular bipartite graphs on n vertices with 3 <= d <= n(c), for a small universal constant c > 0. We prove that the chain satisfies a Poincare inequality with a constant of order O(nd); moreover, when d is fixed, we establish a log-Sobolev inequality for the chain with a constant of order O-d(n log n). We show that both results are optimal. The Poincare inequality implies that in the regime 3 <= d <= n(c) the mixing time of the switch chain is at most ...
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作者：Balint, Peter; Bruin, Henk; Terhesiu, Dalia
作者单位：Budapest University of Technology & Economics; MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; University of Vienna; Leiden University; Leiden University - Excl LUMC
摘要：We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size rho may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well studied regimes with superdiffusive root n log n scaling (i) for fixed infi...
