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作者：Budzinski, Thomas; Louf, Baptiste
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Uppsala University
摘要：We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence toward a family of infinite maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property and a hyperbolic behaviour. Therefore, we observe a similar local behaviour for a wide class of models of random high genus maps which can be seen as a result of universality. Our results cover all the regimes where the expected degree of the root face remains finite in the ...
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Gaussian multiplicative chaos (GMC) is informally defined as a random measure e(gamma X) dx where X is Gaussian field on R-d (or an open subset of it) whose correlation function is of the form K(x, y) = log 1/vertical bar y-x vertical bar + L(x, y), where L is a continuous function of x and y and gamma = alpha + i beta is a complex parameter. In the present paper we consider the case gamma is an element of P-III', where P-III':= {alpha + i beta : alpha, gamma is an element of R, vertical bar a...
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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：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：Ioffe, Dmitry; Ott, Sebastien; Shlosman, Senya; Velenik, Yvan
作者单位：Technion Israel Institute of Technology; Roma Tre University; University of Geneva
摘要：In this paper, we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N x N rectangular box with a boundary condition inducing the coexistence of the + phase in the bulk and a layer of - phase along the bottom wall. The presence of an external magnetic field of intensity h = lambda/N (for some fixed lambda > 0) makes the layer of - phase unstable. For any beta > beta(c), w...
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作者：Cerrai, Sandra; Xi, Guangyu
作者单位：University System of Maryland; University of Maryland College Park
摘要：We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of R-n subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass limit the solution converges to the solution of a stochastic quasilinear parabolic equation where a noise-induced extra drift is created.
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作者：Dyszewski, Piotr; Gantert, Nina; Johnston, Samuel G. G.; Prochno, Joscha; Schmid, Dominik
作者单位：Technical University of Munich; University of Bath; University of Passau
摘要：We study the asymptotics of the k-regular self-similar fragmentation process. For alpha > 0 and an integer k >= 2, this is the Markov process (I-t)(t >= 0) in which each I-t is a union of open subsets of [0, 1), and independently each subinterval of I-t of size u breaks into k equally sized pieces at rate u(alpha). Let k(-mt) and k(-Mt) be the respective sizes of the largest and smallest fragments in I-t. By relating (I-t)(t >= 0) to a branching random walk, we find that there exist explicit d...
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作者：Berger, Noam; Cohen, Moran; Deuschel, Jean-Dominique; Guo, Xiaoqin
作者单位：Technical University of Munich; Hebrew University of Jerusalem; Technical University of Berlin; University System of Ohio; University of Cincinnati
摘要：We prove an elliptic Harnack inequality at large scale on the lattice Z(d) for nonnegative solutions of a difference equation with balanced i.i.d. coefficients which are not necessarily elliptic. We also identify the optimal constant in the Harnack inequality. Our proof relies on a quantitative homogenization result of the corresponding invariance principle to Brownian motion and on percolation estimates. As a corollary of our main theorem, we derive an almost optimal Holder estimate.
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作者：Dunlap, Alexander; Gu, Yu
作者单位：New York University; University System of Maryland; University of Maryland College Park
摘要：We consider a nonlinear stochastic heat equation in spatial dimension d = 2, forced by a white-in-time multiplicative Gaussian noise with spatial correlation lengths epsilon > 0 but divided by a factor of root log epsilon(-1). We impose a condition on the Lipschitz constant of the nonlinearity so that the problem is in the weak noise regime. We show that, as epsilon down arrow 0, the one-point distribution of the solution converges, with the limit characterized in terms of the solution to a fo...
