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作者：Nica, Mihai; Quastel, Jeremy; Remenik, Daniel
作者单位：University of Toronto; Universidad de Chile; Universidad de Chile
摘要：We provide a direct and elementary proof that the formula obtained in (Matetski, Quastel and Remenik (2016)) for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.
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作者：Doering, Leif; Kyprianou, Andreas E.
作者单位：University of Mannheim; University of Bath
摘要：In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on - infinity <= a < b <= infinity in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the boundary. Feller's technique is restricted to diffusion processes as the corresponding differential generators allow explicit computations and the use of Hille-Yosida theory. In the present article, we study exit and entrance from infinity for the most na...
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作者：Guionnet, Alice; Husson, Jonathan
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：In this article, we consider random Wigner matrices, that is, symmetric matrices such that the subdiagonal entries of X-n are independent, centered and with variance one except on the diagonal where the entries have variance two. We prove that, under some suitable hypotheses on the laws of the entries, the law of the largest eigenvalue satisfies a large deviation principle with the same rate function as in the Gaussian case. The crucial assumption is that the Laplace transform of the entries m...
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作者：Huang, Jiaoyang; Landon, Benjamin; Yau, Horng-Tzer
作者单位：Harvard University
摘要：We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erdos-Renyi graph G(N, p). Tracy-Widom fluctuations of the extreme eigenvalues for p >> N-2/3 was proved in (Probab. Theory Related Fields 171 (2018) 543-616; Comm. Math. Phys. 314 (2012) 587-640). We prove that there is a crossover in the behavior of the extreme eigenvalues at p similar to N-2/3. In the case that N-7/9 << p << N-2/3...
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作者：Backhoff-Veraguas, Julio; Beiglboeck, Mathias; Huesmann, Martin; Kallblad, Sigrid
作者单位：University of Twente; University of Vienna; Royal Institute of Technology
摘要：In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are corner-stones of the field and form the basis for a variety of applications in other mathematical areas. We suggest a Benamou-Brenier type formulation of the martingale transport problem for given d-dimensional distributions mu, nu in convex order. The unique solution M* = (M-t*)(t is an element of[0,1]) of this problem turns out to be a Markov-martingale whic...
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作者：Hutzenthaler, Martin; Jentzen, Arnulf
作者单位：University of Duisburg Essen; University of Munster
摘要：We develop a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the L-p-distance between the solution process of an SDE and an arbitrary Ito process, which we view as a perturbation of the solution process of the SDE, by the L-q-distances of the differences of the local characteristics for suitable p, q > 0. As one application ...
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作者：Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Stanford University
摘要：We consider the limit of a linear kinetic equation with reflection-transmission-absorption at an interface and with a degenerate scattering kernel. The equation arises from a microscopic chain of oscillators in contact with a heat bath. In the absence of the interface, the solutions exhibit a superdiffusive behavior in the long time limit. With the interface, the long time limit is the unique solution of a version of the fractional in space heat equation with reflection-transmission-absorption...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Saclay
摘要：We consider the model of Brownian motion indexed by the Brownian tree. For every r >= 0 and every connected component of the set of points where Brownian motion is greater than r, we define the boundary size of this component, and we then show that the collection of these boundary sizes evolves when r varies like a well-identified growth-fragmentation process. We then prove that the same growth-fragmentation process appears when slicing a Brownian disk at height r and considering the perimeter...
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作者：Dembin, Barbara
作者单位：Universite Paris Cite
摘要：We consider the standard first passage percolation model on Z(d) with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R-d and infinity. The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut A from infinity. We prove that the rescaled maximal flow between nA and infinity phi(nA)/n(d-1) almost surely converges toward a deterministic constant depending on A. This constant corres...
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作者：Janjigian, Christopher; Rassoul-Agha, Firas
作者单位：Utah System of Higher Education; University of Utah
摘要：We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/nonuniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin-Lanford-Ruelle equations). We also prove nonexistence of covariant or deterministically directed ...
