Probability Theory and Related Fields

最新文章

• Deviation results for sparse tables in hashing with linear probing AI翻译
  作者：Klein, Thierry; Lagnoux, Agnes; Petit, Pierre
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite de Toulouse; Universite de Toulouse - Jean Jaures; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：We consider the model of hashing with linear probing and we establish the moderate and large deviations for the total displacement in sparse tables. In this context, Weibull-like-tailed random variables appear. Deviations for sums of such heavy-tailed random variables are studied in Nagaev (Theory Probab Appl 14(1):51-64, 1969; Theory Probab Appl 14(2):193-208, 1969). Here we adapt the proofs therein to deal with conditioned sums of such variables and solve the open question in Gamboa et al. (...
• Exceptional points of two-dimensional random walks at multiples of the cover time AI翻译
  作者：Abe, Yoshihiro; Biskup, Marek
  作者单位：Chiba University; University of California System; University of California Los Angeles
  摘要：We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by N) versions D-N subset of Z(2) of bounded open domains D subset of R-2. Upon exit from D-N, the walk lands on a boundary vertex and then reenters D-N through a random boundary edge in the next step. In the parametrization by the local time at the boundary vertex we prove that, at times corresponding to a theta-multiple of the cover time of D-N, the sets of suitably defined lambda-thick (i.e.,...
• Dynamic polymers: invariant measures and ordering by noise AI翻译
  作者：Bakhtin, Yuri; Chen, Hong-Bin
  作者单位：New York University
  摘要：We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1 + 1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the...
• Hydrodynamic limit of simple exclusion processes in symmetric random environments via duality and homogenization AI翻译
  作者：Faggionato, Alessandra
  作者单位：Sapienza University Rome
  摘要：We consider continuous-time random walks on a random locally finite subset of R d with random symmetric jump probability rates. The jump range can be unbounded. We assume some second-moment conditions and that the above randomness is left invariant by the action of the group G = R-d or G = Z(d). We then add a site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits...
• Quasi-static limit for the asymmetric simple exclusion AI翻译
  作者：De Masi, Anna; Marchesani, Stefano; Olla, Stefano; Xu, Lu
  作者单位：University of L'Aquila; Gran Sasso Science Institute (GSSI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France
  摘要：We study the one-dimensional asymmetric simple exclusion process on the lattice (1, ..., N) with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale N-a with a > 0. We prove that at the time scale N1+a the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates....
• Accelerating abelian random walks with hyperbolic dynamics AI翻译
  作者：Dubail, Bastien; Massoulie, Laurent
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
  摘要：Given integers d >= 2, n >= 1, we consider affine random walks on torii (Z/nZ)(d) defined as Xt+1 = AX(t) + B-t mod n, where A is an element of GL(d)(Z) is a invertible matrix with integer entries and (B-t)(t >= 0) is a sequence of iid random increments on Z(d). We show that when A has no eigenvalues of modulus 1, this random walk mixes in O (log n log log n) steps as n -> infinity, and mixes actually in O (log n) steps only for almost all n. These results are similar to those of Chung et al. ...
• Planarity and non-separating cycles in uniform high genus quadrangulations AI翻译
  作者：Louf, Baptiste
  作者单位：Uppsala University
  摘要：We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.
• Entropy-Transport distances between unbalanced metric measure spaces AI翻译
  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...
• Multi-point distribution of discrete time periodic TASEP AI翻译
  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...
• Convergence of the spectral radius of a random matrix through its characteristic polynomial AI翻译
  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...