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作者：Baxendale, Peter; Wong, Ting-Kam Leonard
作者单位：University of Southern California; University of Toronto
摘要：Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gradient maps define novel investment strategies. The gradient maps may also be regarded as optimal transport maps on the simplex. In this paper we construct and study probability ...
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作者：Racz, Miklos Z.; Sridhar, Anirudh
作者单位：Princeton University
摘要：We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly growing graphs, such as uniform attachment (UA) or preferential attachment (PA). Given such a model, a pair of graphs (G(1), G(2)) is grown in two stages: until time t(*) they are grown together (i.e., G(1) = G(2)), after which they grow independently according to...
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作者：Baldasso, Rangel; Pereira, Alan; Reis, Guilherme
作者单位：Bar Ilan University; Universidade Federal de Alagoas; Universidade Federal da Bahia
摘要：We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the path-dependent McKean-Vlasov diffusion associated t...
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作者：Coja-Oghlan, Amin; Mueller, Noela; Ravelomanan, Jean B.
作者单位：Dortmund University of Technology; Eindhoven University of Technology
摘要：Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as replica symmetry in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model...
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作者：Fredes, Luis; Linker, Amitai; Remenik, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universidad Andres Bello; Universidad de Chile; Universidad de Chile
摘要：We investigate the effect on survival and coexistence of introducing forest fire epidemics to a certain two-species competition model. The model is an extension of the one introduced by Durrett and Remenik (Ann. Appl. Probab. 19 (2009) 1656-1685), who studied a discrete time particle system running on a random 3-regular graph where occupied sites grow until they become sufficiently dense so that an epidemic wipes out large clusters. In our extension we let two species affected by independent e...
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作者：Conforti, Giovanni
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We study the exponential dissipation of entropic functionals along the semigroup generated by a continuous time Markov chain and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry-Emery approach and coupling arguments, which we use as a probabilistic alternative to the discrete Bochner identities. In particular, the validity of the method is not limited to the perturbative setting and we establish convex entropy deca...
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作者：Hening, Alexandru; Nguyen, Dang H.; Schreiber, Sebastian J.
作者单位：Tufts University; University of Alabama System; University of Alabama Birmingham; University of California System; University of California Davis
摘要：The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is determined by a finite number of stationary distributions. In this paper we consider the classification problem for stochastic models of interacting species. For a large class of three-species, stochastic differential equation models, we prove a variant of Palis' c...
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作者：Qin, Qian; Hobert, James P.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Florida
摘要：Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity analysis, which is the study of how the convergence behavior of Monte Carlo Markov chains scales with sample size, n, and/or number of covariates, p. The problem appears to be that minorization can become a serious liability as dimension in...
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作者：Campi, Luciano; De Angelis, Tiziano; Ghio, Maddalena; Livieri, Giulia
作者单位：University of Milan; University of Turin; Collegio Carlo Alberto; Scuola Normale Superiore di Pisa
摘要：We study Nash equilibria for a sequence of symmetric N-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equi...
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作者：Jain, Vishesh; Pillai, Natesh S.; Sah, Ashwin; Sawhney, Mehtaab; Smith, Aaron
作者单位：Stanford University; Harvard University; Massachusetts Institute of Technology (MIT); University of Ottawa
摘要：In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For n points in R-d, we design an optimal Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be applied to any vector in time O(d log d) for essentially the same restriction on n as in the best-known transforms due to Ailon and Liberty, and Bamberger and Krahmer. Our algorithm is memory-optimal, and outperforms existing algorithms in regimes when n is sufficiently large an...
