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作者：Henning, Florian; Kulske, Christof
作者单位：Ruhr University Bochum
摘要：We study gradient models for spins taking values in the integers (or an integer lattice), which interact via a general potential depending only on the differences of the spin values at neighboring sites, located on a regular tree with d + 1 neighbors. We first provide general conditions in terms of the relevant p-norms of the associated transfer operator Q which ensure the existence of a countable family of proper Gibbs measures, describing localization at different heights. Next we prove exis...
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作者：Mangoubi, Oren; Smith, Aaron
作者单位：Worcester Polytechnic Institute; University of Ottawa
摘要：We obtain several quantitative bounds on the mixing properties of an ideal Hamiltonian Monte Carlo (HMC) Markov chain for a strongly log-concave target distribution pi on R-d. Our main result says that the HMC Markov chain generates a sample with Wasserstein error epsilon in roughly O(kappa(2) log(1/epsilon)) steps, where the condition number kappa = M-2/m(2) is the ratio of the maximum M-2 and minimum m(2) eigenvalues of the Hessian of - log(pi). In particular, this mixing bound does not depe...
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作者：Du, Qiming; Guyader, Arnaud
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Sorbonne Universite
摘要：Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels usually depend on tuning parameters that are of first importance for the efficiency of the algorithm. A standard way to address this problem is to apply adaptive sequential Monte Carlo (ASMC) methods, which consist in exploiting the information given by the hist...
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作者：Tomasevic, Milica
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Recently, we proposed a new stochastic interpretation of the parabolic-parabolic Keller-Segel system without cut-off via a McKean-Vlasov stochastic process. The process was defined through an original type of interaction kernel which involved, in a singular way, all its past time marginal distributions. In the present paper, we study this McKean-Vlasov representation in the two-dimensional case. In this setting, there exists a possibility of a blow-up in finite time for the Keller-Segel system...
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作者：Andrieu, Christophe; Durmus, Alain; Nusken, Nikolas; Roussel, Julien
作者单位：University of Bristol; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Imperial College London; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria
摘要：In this work, we establish L-2-exponential convergence for a broad class of piecewise deterministic Markov processes recently proposed in the context of Markov process Monte Carlo methods and covering in particular the randomized Hamiltonian Monte Carlo (Trans. Amer. Math. Soc. 367 (2015) 3807-3828; Ann. Appl. Probab. 27 (2017) 2159-2194), the zig-zag process (Ann. Statist. 47 (2019) 1288-1320) and the bouncy particle Sampler (Phys. Rev. E 85 (2012) 026703; J. Amer. Statist. Assoc. 113 (2018) ...
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作者：Athreya, Siva; den Hollander, Frank; Rollin, Adrian
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Leiden University; Leiden University - Excl LUMC; National University of Singapore
摘要：The goal of this paper is to construct a natural class of graphon-valued processes arising from population genetics. We consider finite populations where individuals carry one of finitely many genetic types and change type according to Fisher-Wright resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current types of the two individuals and on the current empirical type distribution of ...
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作者：Janson, Svante; Warnke, Lutz
作者单位：Uppsala University; University System of Georgia; Georgia Institute of Technology
摘要：We study the following preferential attachment variant of the classical Erd os-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly proportional to the product of the current degrees of its endpoints (note that the vertex set is fixed). We determine the asymptotic size of the giant component in the supercritical phase, confirming a conjecture of Pittel from 2010. Our proof uses a simple ...
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作者：Bielecki, Tomasz R.; Jakubowski, Jacek; Jeanblanc, Monique; Nieweglowski, Mariusz
作者单位：Illinois Institute of Technology; University of Warsaw; Universite Paris Saclay; Warsaw University of Technology
摘要：We consider a complete probability space (Omega, F, P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F subset of G. On this probability space we consider a real valued Gsemimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compu...
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作者：McVinish, Ross; Hodgkinson, Liam
作者单位：University of Queensland
摘要：Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we propose a new method for approximate simulation of spin systems which approximates the evolution of spin at each site between sampling epochs as an independent two-state Markov chain. Whe...
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作者：Fang, Xiao; Koike, Yuta
作者单位：Chinese University of Hong Kong; University of Tokyo
摘要：We obtain explicit error bounds for the d-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a nonlinear statistic of independent random variables or a sum of n locally dependent random vectors. We assume the approximating normal distribution has a nonsingular covariance matrix. The error bounds vanish even when the dimension d is much larger than the sample size n. We prove our main results using the ...
