Probability Theory and Related Fields

最新文章

• Gaussian unitary ensemble in random lozenge tilings AI翻译
  作者：Aggarwal, Amol; Gorin, Vadim
  作者单位：Columbia University; University of California System; University of California Berkeley
  摘要：This paper establishes a universality result for scaling limits of uniformly random lozenge tilings of large domains. We prove that whenever the boundary of the domain has three adjacent straight segments inclined under 120 degrees (measured in the direction internal to the domain) to each other, the asymptotics of tilings near the middle segment is described by the GUE-corners process of random matrix theory. An important step in our argument is to show that fluctuations of the height functio...
• Approximation of martingale couplings on the line in the adapted weak topology AI翻译
  作者：Beiglboeck, M.; Jourdain, B.; Margheriti, W.; Pammer, G.
  作者单位：University of Vienna; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Our main result is to establish stability of martingale couplings: suppose that pi is a martingale coupling with marginals mu, nu. Then, given approximating marginal measures (mu) over tilde approximate to mu, (nu) over tilde approximate to nu in convex order, we show that there exists an approximating martingale coupling (pi) over tilde approximate to pi with marginals (mu) over tilde, (nu) over tilde. In mathematical finance, prices of European call/put option yield information on the margin...
• Fully-connected bond percolation on Zd AI翻译
  作者：Dereudre, David
  作者单位：Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We consider the bond percolation model on the lattice Z(d) (d >= 2) with the constraint to be fully connected. Each edge is open with probability p is an element of (0, 1), closed with probability 1- p and then the process is conditioned to have a unique open connected component (bounded or unbounded). The model is defined on Z(d) by passing to the limit for a sequence of finite volume modelswith general boundary conditions. Several questions and problems are investigated: existence, uniquenes...
• Non-uniformly parabolic equations and applications to the random conductance model AI翻译
  作者：Bella, Peter; Schaeffner, Mathias
  作者单位：Dortmund University of Technology
  摘要：We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on Z(d). In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.
• The local limit of uniform spanning trees AI翻译
  作者：Nachmias, Asaf; Peres, Yuval
  作者单位：Tel Aviv University; University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
  摘要：We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching process conditioned to survive forever. An extension to almost regular graphs and a quenched version are also given.
• Cutoff profiles for quantum Levy processes and quantum random transpositions AI翻译
  作者：Freslon, Amaury; Teyssier, Lucas; Wang, Simeng
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Vienna; Harbin Institute of Technology
  摘要：We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time N ln(N). Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semicircle law. We prove similar results for quantum permutations and quantum random transpositions.
• Grassmannian stochastic analysis and the stochastic quantization of Euclidean fermions AI翻译
  作者：Albeverio, Sergio; Borasi, Luigi; De Vecchi, Francesco C.; Gubinelli, Massimiliano
  作者单位：University of Bonn
  摘要：We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum probability: a Grassmann random variable is an homomorphism of an abstract Grassmann algebra into a quantum probability space, i.e. a C*-algebra endowed with a suitable state. We define the notion of Gaussian processes, Brownian motion and stochastic (partial) d...
• Number of paths in oriented percolation as zero temperature limit of directed polymer AI翻译
  作者：Fukushima, Ryoki; Junk, Stefan
  作者单位：University of Tsukuba; Tohoku University
  摘要：We prove that the free energy of directed polymer in Bernoulli environment converges to the growth rate for the number of open paths in super-critical oriented percolation as the temperature tends to zero. Our proof is based on rate of convergence results which hold uniformly in the temperature. We also prove that the convergence rate is locally uniform in the percolation parameter inside the super-critical phase, which implies that the growth rate depends continuously on the percolation param...
• Mapping TASEP back in time AI翻译
  作者：Petrov, Leonid; Saenz, Axel
  作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia; University of Warwick
  摘要：We obtain a new relation between the distributions mu(t) at different times t >= 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions mu(t) backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammers...
• Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema AI翻译
  作者：Kosygina, Elena; Mountford, Thomas; Peterson, Jonathon
  作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
  摘要：We consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motion perturbed at its extrema (BMPE). All parameters of the limiting process are given explicitly in terms of those of the cookie Markov chain at a single site. While our results extend the results in Dolgopyat and Kosygina (Electron Commun Prob...