-
作者：De Ponti, Nicolo; Mondino, Andrea
作者单位：International School for Advanced Studies (SISSA); University of Oxford
摘要：Inspired by the recent theory of Entropy-Transport problems and by the D-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly different total mass. We provide several explicit examples of such distances, where a prominent role is played by a geodesic metric based on the Hellinger-Kantorovich distance. Moreover, we discuss some limiting cases of the theory, recovering the pure transport D-dista...
-
作者：Liao, Yuchen
作者单位：University of Warwick
摘要：We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint di...
-
作者：Bordenave, Charles; Chafai, Djalil; Garcia-Zelada, David
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine
摘要：Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in probability. This result can also be seen as the convergence of the support in the circular law theorem under optimal moment conditions. In the proof we establish the convergence in law of the reciprocal characteristic polynomial to a random analytic function...
-
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...
-
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...
-
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...
-
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.
-
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.
-
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.
-
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...
