2024

最新文章

• SPECTRAL GAP OF THE SYMMETRIC INCLUSION PROCESS AI翻译
  作者：Kim, Seonwoo; Sau, Federico
  作者单位：Korea Institute for Advanced Study (KIAS); University of Trieste
  摘要：We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulate...
• 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....
• A TWO-TABLE THEOREM FOR A DISORDERED CHINESE RESTAURANT PROCESS AI翻译
  作者：Bjornberg, Jakob E.; Mailler, Cecile; Moerters, Peter; Ueltschi, Daniel
  作者单位：Chalmers University of Technology; University of Gothenburg; University of Bath; University of Cologne; University of Warwick
  摘要：We investigate a disordered variant of Pitman's Chinese restaurant process where tables carry i.i.d. weights. Incoming customers choose to sit at an occupied table with a probability proportional to the product of its occupancy and its weight, or they sit at an unoccupied table with a probability proportional to a parameter 6 > 0. This is a system out of equilibrium where the proportion of customers at any given table converges to zero almost surely. We show that for weight distributions in an...
• THE COALESCENT STRUCTURE OF GALTON-WATSON TREES IN VARYING ENVIRONMENTS AI翻译
  作者：Harris, Simon c.; Palau, Sandra; Pardo, Juan carlos
  作者单位：University of Auckland; Universidad Nacional Autonoma de Mexico
  摘要：We investigate the genealogy of a sample of k >= 2 particles chosen uniformly without replacement from a population alive at large times in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coales...
• MARTINGALE TRANSPORTS AND MONGE MAPS AI翻译
  作者：Nutz, Marcel; Wang, Ruodu; Zhang, Zhenyuan
  作者单位：Columbia University; University of Waterloo; Stanford University
  摘要：It is well known that martingale transport plans between marginals mu not equal nu are never given by Monge maps-with the understanding that the map is over the first marginal mu, or forward in time. Here, we change the perspective, with surprising results. We show that any distributions mu, nu in convex order with nu atomless admit a martingale coupling given by a Monge map over the second marginal nu. Namely, we construct a particular coupling called the barcode tingale transports are dense ...
• HARMONIC MEASURE IN A MULTIDIMENSIONAL GAMBLER'S PROBLEM AI翻译
  作者：Denisov, Denis; Wachtel, Vitali
  作者单位：University of Manchester; University of Bielefeld
  摘要：We consider a random walk in a truncated cone KN, which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study the behaviour of the Green function in this truncated cone as N increases. Using these results we also obtain the asymptotic behaviour of the harmonic The obtained results are applied to a multidimensional gambler's problem studied by Diaconis and Ethier (Staist. Sci. 37 (2022) 289-305). In particular we confirm their conjecture that the probability of e...
• THE MODIFIED MSA, A GRADIENT FLOW AND CONVERGENCE AI翻译
  作者：Sethi, Deven; Siska, David
  作者单位：University of Edinburgh
  摘要：The modified method of successive approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin optimality principle which, starting with an initial open loop control, solves the forward equation, the backward adjoint equation and then performs a static minimization step. We observe that this is an implicit Euler scheme for a gradient flow system. We prove that appropriate interpolations of the iterates of the modi...
• ERGODICITY OF THE UNDERDAMPED MEAN-FIELD LANGEVIN DYNAMICS AI翻译
  作者：Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian
  作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong; Technische Universitat Wien
  摘要：We study the long time behavior of an underdamped mean -field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide some numerical examples of the algorithm to train a generative adversarial network (GAN).
• AN EXPLICIT MILSTEIN-TYPE SCHEME FOR INTERACTING PARTICLESYSTEMS AND MCKEAN-VLASOV SDES WITH COMMON NOISE ANDNON-DIFFERENTIABLE DRIFT COEFFICIENTS AI翻译
  作者：Biswas, Sani; Kumar, Chaman; Neelima; Dos Reis, Goncalo; Reisinger, Christoph
  作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Edinburgh; University of Oxford
  摘要：We propose an explicit drift-randomised Milstein scheme for bothMcKean-Vlasov stochastic differential equations and associated high-dimen-sional interacting particle systems with common noise. By using a driftrandomisation step in space and measure, we establish the scheme's strongconvergence rate of 1 under reduced regularity assumptions on the drift co-efficient: no classical (Euclidean) derivatives in space or measure derivatives(e.g., Lions/Frechet) are required. The main result is establi...
• ON r-TO-p NORMS OF RANDOM MATRICES WITH NONNEGATIVE ENTRIES: ASYMPTOTIC NORMALITY AND l∞-BOUNDS FOR THE MAXIMIZER AI翻译
  作者：Dhara, Souvik; Mukherjee, Debankur; Ramanan, Kavita
  作者单位：University System of Georgia; Georgia Institute of Technology; Brown University
  摘要：For an nxn matrix A(n), the r -> p operator norm is defined as parallel to An parallel to(r -> p):= sup(x is an element of R)(n):parallel to x parallel to r(<= 1)(n)(parallel to A)x parallel to(p) for r,p >= 1. For different choices of r and p, this norm corresponds to key quantities that arise in diverse applications including matrix condition number estimation, clustering of data, and construction of oblivious routing schemes in transportation networks. This article considers r -> p norms of...