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作者：Ball, Frank
作者单位：University of Nottingham
摘要：We consider a stochastic SIR (susceptible -> infective -> recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph during an infectious period which has an arbitrary but specified distribution. Central limit theorems for the final size (number of initial susceptibles that become infected) of such an epidemic as the population size n tends to infinity, with explicit, easy to compute expressions for the asympt...
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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：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) ...
