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作者：Powell, Ellen
摘要：We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary D. It is known that any such process undergoes a phase transition when the branching rate exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under ...
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作者：Dembo, Amir; Ding, Jian; Miller, Jason; Peres, Yuval
作者单位：Stanford University; University of Pennsylvania; University of Cambridge; Microsoft
摘要：Given a finite, connected graph G, the lamplighter chain on G is the lazy random walk X on the associated lamplighter graph G=Z2G. The mixing time of the lamplighter chain on the torus Zndis known to have a cutoff at a time asymptotic to the cover time of Zndif d=2, and to half the cover time if d3. We show that the mixing time of the lamplighter chain on Gn(a)=Zn2xZalogn has a cutoff at (a) times the cover time of Gn(a) as n, where is an explicit weakly decreasing map from (0,) onto [1/2,1). ...
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作者：Ambrosio, Luigi; Stra, Federico; Trevisan, Dario
作者单位：Scuola Normale Superiore di Pisa; University of Pisa
摘要：We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge-Ampere equation.
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作者：Bally, Vlad; Caramellino, Lucia; Poly, Guillaume
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); University of Rome Tor Vergata; Universite de Rennes
摘要：In this article, we consider the following family of random trigonometric polynomials pn(t,Y)=Sigma k=1nYk1cos(kt)+Yk2sin(kt) for a given sequence of i.i.d. random variables Yki, i is an element of{1,2}, k >= 1, which are centered and standardized. We set N([0,pi],Y) the number of real roots over [0,pi] and N([0,pi],G) the corresponding quantity when the coefficients follow a standard Gaussian distribution. We prove under a Doeblin's condition on the distribution of the coefficients that lim (...
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作者：Benoist, T.; Fraas, M.; Pautrat, Y.; Pellegrini, C.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); KU Leuven; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices, and is then given by a random product of correlated matrices taken from the support of the defining measure. We give natural conditions on this support that imply that the Markov chain admits a unique invariant probability measure. We moreover prove the geometric convergence towards this invariant meas...
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作者：Imamura, Takashi; Sasamoto, Tomohiro
作者单位：Chiba University; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We consider the q-totally asymmetric simple exclusion process (q-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be studied as a limiting case of an N-particle q-TASEP with a random initial condition and with particle dependent hopping rate. Then we explain how this N-particle q-TASEP can be encoded in a dynamics on a two-sided Gelfand-Tsetlin cone described by a two-sided q-Whittaker process and present a Fredholm ...
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作者：Huang, Jiaoyang; Landon, Benjamin
作者单位：Harvard University
摘要：We study Dyson Brownian motion with general potential V and for general beta >= 1. For short times t = o(1) and under suitable conditions on V we obtain a local law and corresponding rigidity estimates on the particle locations; that is, with overwhelming probability, the particles are close to their classical locations with an almost-optimal error estimate. Under the condition that the density of states of the initial data is bounded below and above down to the scale eta(*) << t << 1, we prov...
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作者：Naumov, Alexey; Spokoiny, Vladimir; Ulyanov, Vladimir
作者单位：HSE University (National Research University Higher School of Economics); Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Lomonosov Moscow State University
摘要：Let X1, ... ,X-n be i.i.d. sample in Rp with zero mean and the covariance matrix Sigma. The problem of recovering the projector onto an eigenspace of Sigma from these observations naturally arises in many applications. Recent technique from Koltchinskii and Lounici (Ann Stat 45(1):121-157,2017) helps to study the asymptotic distribution of the distance in the Frobenius norm parallel to P-r-(P) over cap (r)parallel to(2) between the true projector Pr on the subspace of the rth eigenvalue and it...
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作者：Kabluchko, Zakhar; Marynych, Alexander; Temesvari, Daniel; Thaele, Christoph
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Ruhr University Bochum
摘要：Let U1, U2,... be random points sampled uniformly and independently from the d-dimensional upper half-sphere. We showthat, as n.8, the f -vector of the (d+1)-dimensional convex cone Cn generated by U1,..., Un weakly converges to a certain limiting random vector, without any normalization. We also show convergence of all moments of the f -vector of Cn and identify the limiting constants for the expectations. We prove that the expected Grassmann angles of Cn can be expressed through the expected...
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作者：Hough, Robert
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorem of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis-Hough which treated general measures on the Heisenberg gr...
