4期

最新文章

• CYLINDERS' PERCOLATION: DECOUPLING AND APPLICATIONS AI翻译
  作者：Alves, Caio; Teixeira, Augusto
  作者单位：United States Department of Energy (DOE); Oak Ridge National Laboratory; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
  摘要：In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch ( Probab. Theory Related Fields 154 (2012) 165-191). This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder's percolation is particularly intricate, given that the cylinders have infinite range (un...
• ASYMPTOTIC PROBABILITY OF ENERGY INCREASING SOLUTIONS TO THE HOMOGENEOUS BOLTZMANN EQUATION AI翻译
  作者：Basile, Giada; Enedetto, Dariob; Bertin, Lorenzo; Caglioti, Emanuele
  作者单位：Sapienza University Rome
  摘要：Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with binary collisions (Kac's model) and show that these solutions are atypical. More precisely, we prove that the probability of observing these paths is exponentially small in the number of particles and compute the exponential rate. This result is obtained by improving the established large deviation estimates in the can...
• A PHASE TRANSITION IN ARROW'S THEOREM WITH THREE ALTERNATIVES AI翻译
  作者：Koehler, Frederic; Mossel, Elchanan
  作者单位：University of Chicago; University of Chicago; Massachusetts Institute of Technology (MIT)
  摘要：Arrow's theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or more candidates, there are situations where any voting rule satisfying a small list of natural fairness axioms must produce an apparently irrational intransitive outcome. Furthermore, quantitative versions of Arrow's theorem in the literature show that when...
• ON THE NUMBER OF CYCLES IN COMMUTATORS OF RANDOM PERMUTATIONS AI翻译
  作者：Dubach, Guillaume
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we derive explicit formulas for the generating functions of the number of cycles in the commutator [ sigma, tau] ] = sigma tau sigma (- 1 )tau (- 1) where sigma is uniformly distributed, and tau is either one cycle, the product of many transpositions, or the product of two cycles of same size, the latter case being a new ...
• ASYMPTOTIC BIAS OF INEXACT MARKOV CHAIN MONTE CARLO METHODS IN HIGH DIMENSION AI翻译
  作者：Durmus, Alain; Eberle, Andreas
  作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; University of Bonn
  摘要：Inexact Markov chain Monte Carlo methods rely on Markov chains that do not exactly preserve the target distribution. Examples include the unadjusted Langevin algorithm (ULA) and unadjusted Hamiltonian Monte Carlo (uHMC). This paper establishes bounds on Wasserstein distances between the invariant probability measures of inexact MCMC methods and their target distributions with a focus on understanding the precise dependence of this asymptotic bias on both dimension and discretization step size....
• UNIVERSALITY OF APPROXIMATE MESSAGE PASSING ALGORITHMS AND TENSOR NETWORKS AI翻译
  作者：Wang, Tianhao; Zhong, Xinyi; Fan, Zhou
  作者单位：Yale University
  摘要：Approximate message passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications. Although these algorithms are often first derived for matrices having independent Gaussian entries or satisfying rotational invariance in law, their state evolution characterizations are expected to hold over larger universality classes of random matrix ensembles. We develop several new results on AMP universality. For AMP algorithms tailored to...
• A REVERSE ERGODIC THEOREM FOR INHOMOGENEOUS KILLED MARKOV CHAINS AND APPLICATION TO A NEW UNIQUENESS RESULT FOR REFLECTING DIFFUSIONS AI翻译
  作者：Costantini, Cristina; Kurtz, Thomas G.
  作者单位：G d'Annunzio University of Chieti-Pescara; G d'Annunzio University of Chieti-Pescara; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：Bass and Pardoux ( Probab. Theory Related Fields (1987) 76 557-572) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub- probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian motion in cones in Kwon and Williams ( Trans. Amer. Math. Soc (1991) 32 739-780) and Taylor and Williams ( Probab. Theory Related Fields (1993) 96 283-317). By a different approach, we are able to prove an analogous reverse ergodic theorem for a...
• RATIO CONVERGENCE RATES FOR EUCLIDEAN FIRST-PASSAGE PERCOLATION: APPLICATIONS TO THE GRAPH INFINITY LAPLACIAN AI翻译
  作者：Bungert, Leon; Calder, Jeff; Roith, Tim
  作者单位：University of Wurzburg; University of Minnesota System; University of Minnesota Twin Cities; Helmholtz Association; Deutsches Elektronen-Synchrotron (DESY)
  摘要：In this paper we prove the first quantitative convergence rates for the graph infinity Laplace equation for length scales at the connectivity threshold. In the graph-based semisupervised learning community this equation is also known as Lipschitz learning. The graph infinity Laplace equation is characterized by the metric on the underlying space, and convergence rates follow from convergence rates for graph distances. At the connectivity threshold, this problem is related to Euclidean first pa...
• THE MAXIMAL DEGREE IN RANDOM RECURSIVE GRAPHS WITH RANDOM WEIGHTS AI翻译
  作者：Lodewijks, Bas; Ortgiese, Marcel
  作者单位：University of Augsburg; University of Bath
  摘要：We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the network, so that a new vertex connects to one of the old vertices with a probability that is proportional to their vertex-weight. We first identify the asymptotic degree distribution of a uniformly chosen vertex for a general vertex-weight distribution. For...
• REPEATED AVERAGES ON GRAPHS AI翻译
  作者：Movassagh, Ramis; Szegedy, Mario; Wang, Guanyang
  作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
  摘要：Sourav Chatterjee, Persi Diaconis, Allan Sly, and Lingfu Zhang (Ann. Probab. 50 (2022) 1-17), prompted by a question of Ramis Movassagh, renewed the study of a process proposed in the early 1980s by Jean Bourgain. A state vector v is an element of R-n, labeled with the vertices of a connected graph, G, changes in discrete time steps following the simple rule that at each step a random edge (i, j) is picked and v(i) and v(j) are both replaced by their average (v(i) + v(j))/2. It is easy to see ...