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作者：Goldman, Michael; Huesmann, Martin
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Munster
摘要：The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given by the solution to the linearized equation that is, the Poisson equation. Moreover, we prove that at all mesoscopic scales, this displacement is close in suitable negative Sobolev spaces to a curl-free Gaussian free field. For this, we combine a quantitative estimate on the difference between the displacement and the ...
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作者：Harris, Simon C.; Horton, Emma; Kyprtanou, Andreas E.; Wang, Minmin
作者单位：University of Auckland; Inria; University of Bath; University of Sussex
摘要：We consider the classical Yaglom limit theorem for a branching Markov process X = (X-t, t >= 0), with nonlocal branching mechanism in the setting that the mean semigroup is critical, that is, its leading eigenvalue is zero. In particular, we show that there exists a constant c(f ) such that Law(< f, X-t >/t < f, X-t > > 0) -> e(c)(f), t -> infinity, where e(c)(f ) is an exponential random variable with rate c(f ) and the con-vergence is in distribution. As part of the proof, we also show that ...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：A point of a metric space is called a geodesic star with m arms if it is the endpoint of m disjoint geodesics. For every m is an element of {1 , 2, 3, 4}, we prove that the set of all geodesic stars with m arms in the Brownian sphere has dimension 5 - m. This complements recent results of Miller and Qian, who proved that this dimension is smaller than or equal to 5 - m.
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作者：Miller, Jason; Sheffield, Scott; Werner, Wendelin
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We show that, when one draws a simple conformal loop ensemble (CLE kappa for kappa is an element of (8/3, 4)) on an independent root kappa-Liouville quantum gravity (LQG) surface and explores the CLE in a natural Markovian way, the quantum surfaces (e.g., corresponding to the interior of the CLE loops) that are cut out form a Poisson point process of quantum disks. This construction allows us to make direct links between CLE on LQG, (4/kappa)-stable processes, and labeled branching trees. The ...
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作者：Dello Schiavo, Lorenzo
作者单位：Institute of Science & Technology - Austria
摘要：We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d >= 2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet-Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 7...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N x N Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws.
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作者：Johansson, Kurt; Rahman, Mustazee
作者单位：Royal Institute of Technology; Durham University
摘要：This article studies the inhomogeneous geometric polynuclear growth model; the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the two-time distribution. Asymptotics of the two-time distribution in the KPZ-scaling limit is then considered, extending to two times several single-time distributions in the KPZ universality class.
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作者：Bowditch, Adam; Sun, Rongfeng
作者单位：National University of Singapore
摘要：In this paper, we construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Furthermore, we show that almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman.
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作者：Conchon-Kerjan, Guillaume
作者单位：Universite Paris Cite
摘要：We prove the cutoff phenomenon for the random walk on random n-lifts of finite weighted graphs, even when the random walk on the base graph c of the lift is not reversible. The mixing time is w.h.p. t(mix) = h(-1) log n, where h is a constant associated to G, namely the entropy of its universal cover. Moreover, this mixing time is the smallest possible among all n-lifts of G. In the particular case where the base graph is a vertex with d/2 loops, d even, we obtain a cutoff for a d-regular rand...
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作者：Hermon, Jonathan; Sly, Allan; Sousi, Perla
作者单位：University of British Columbia; Princeton University; University of Cambridge
摘要：We establish universality of cutoff for simple random walk on a class of random graphs defined as follows. Given a finite graph G = (V, E) with vertical bar V vertical bar even we define a random graph G* = (V, E U E') obtained by picking E' to be the (unordered) pairs of a random perfect matching of V. We show that for a sequence of such graphs G(n) of diverging sizes and of uniformly bounded degree, if the minimal size of a connected component of G(n) is at least 3 for all n, then the random...
