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作者：Crane, Edward; Rath, Balazs; Yeo, Dominic
作者单位：University of Bristol; MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; University of Oxford
摘要：We study the distribution of ages in the mean field forest fire model introduced by Rath and Toth. This model is an evolving random graph whose dynamics combine Erdos-Renyi edge-addition with a Poisson rain of lightning strikes. All edges in a connected component are deleted when any of its vertices is struck by lightning. We consider the asymptotic regime of lightning rates for which the model displays self-organized criticality. The age of a vertex increases at unit rate, but it is reset to ...
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作者：Ghoussoub, Nassif; Kim, Young-Heon; Palmer, Aaron Zeff
作者单位：University of British Columbia
摘要：We provide a solution to the problem of optimal transport by Brownian martingales in general dimensions whenever the transport cost satisfies certain subharmonic properties in the target variable as well as a stochastic version of the standard twist condition frequently used in deterministic Monge transport theory. This setting includes, in particular, the case of the distance cost c(x, y) = | x - y|. We prove existence and uniqueness of the solution and characterize it as the first time Brown...
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作者：Beffara, Vincent; Peltola, Eveliina; Wu, Hao
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Bonn; Tsinghua University
摘要：This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and similarly, global multiple SLEs describe scaling limits of collections of interfaces in critical lattice models with alternating boundary conditions. In this article, we give a minimal amount of characterizing properties for the global multiple SLEs: we prove...
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作者：Bou-Rabee, Ahmed
作者单位：University of Chicago
摘要：We prove that Abelian sandpiles with random initial states converge almost surely to unique scaling limits. The proof follows the Armstrong-Smart program for stochastic homogenization of uniformly elliptic equations. Using simple random walk estimates, we prove an analogous result for the divisible sandpile and identify its scaling limit as exactly that of the averaged divisible sandpile. As a corollary, this gives a new quantitative proof of known results on the stabilizability of Abelian san...
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作者：Jain, Vishesh; Sah, Ashwin; Sawhney, Mehtaab
作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
摘要：We show that every matrix A is an element of R-n(xn) is, at least, delta parallel to A parallel to-close to a real matrix A + E is an element of R-nxn whose eigenvectors have condition number, at most, (O) over tilde (n)(delta(-1)). In fact, we prove that, with high probability, taking E to be a sufficiently small multiple of an i.i.d. real sub-Gaussian matrix of bounded density suffices. This essentially confirms a speculation of Davies and of Banks, Kulkarni, Mukherjee and Srivastava, who re...
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
摘要：There is a slight gap and error in Remark 3.4 of Ann. Probab. 41, no. 5 (2013), 3284-3305, that was not noticed before the first errata were published (Ann. Probab. 46, no. 4 (2018), 2400-2405). We take this opportunity to provide some additional updates as well.
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作者：Priola, Enrico
作者单位：University of Pavia
摘要：We show uniqueness in law for the critical SPDE dX(t) = AX(t) dt + (-A)(1/2) F(X(t)) dt + dW(t), X-0 = x is an element of H, where A : dom(A) subset of H -> H is a negative definite self-adjoint operator on a separable Hilbert space H having A(-1) of trace class and W is a cylindrical Wiener process on H. Here, F : H -> H can be continuous with, at most, linear growth (some functions F which grow more than linearly can also be considered). This leads to new uniqueness results for generalized s...
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作者：Tolomeo, Leonardo
作者单位：University of Bonn
摘要：We study the two-dimensional wave equation with cubic nonlinearity posed on R-2 with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for initial data in H-s, s > 4/5.
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作者：Dario, Paul; Gu, Chenlin
作者单位：Tel Aviv University; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the heat kernel and the Green's function on the infinite supercritical percolation cluster in dimension d >= 2 and prove a quantitative homogenization theorem for these functions with an almost optimal rate of convergence. These results are a quantitative version of the local central limit theorem proved by Barlow and Hambly in (Electron. J. Probab. 14 (2009) 127). The proof relies on a structure of renormalization for the infinite percolation cluster introduced in (Comm. Pure Appl. M...
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作者：Perkowski, Nicolas; Rosati, Tommaso
作者单位：Free University of Berlin
摘要：We study the scaling limit of a branching random walk in static random environment in dimension d = 1, 2 and show that it is given by a superBrownian motion in a white noise potential. In dimension 1 we characterize the limit as the unique weak solution to the stochastic PDE partial derivative t mu=(Delta+xi)mu+root 2 nu mu xi for independent space white noise xi and space-time white noise (xi) over tilde. In dimension 2 the study requires paracontrolled theory and the limit process is describ...
