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作者：Arapostathis, Ari; Biswas, Anup
作者单位：University of Texas System; University of Texas Austin; Indian Institute of Science Education & Research (IISER) Pune
摘要：We consider a class of diffusions controlled through the drift and jump size, and driven by a jump Levy process and a nondegenerate Wiener pro-cess, and we study infinite horizon (ergodic) risk-sensitive control problems for this model. We start with the controlled Dirichlet eigenvalue problem in smooth bounded domains, which also allows us to generalize current results in the literature on exit rate control problems. Then we consider the infi-nite horizon average risk-sensitive minimization a...
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作者：Finn, Thomas; Stauffer, Alexandre
作者单位：University of Bath; Roma Tre University
摘要：We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are initially vacant. Once a site is occupied by type 1, it converts to type 2 at rate p > 0. Sites occupied by type 2 then spread at rate lambda > 0 through vacant sites and sites occupied by type 1, whereas type 1 can only spread through vacant sites. If the set of sites occ...
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作者：Berger, Noam; Procaccia, Eviatar B.; Turner, Amanda
作者单位：Technical University of Munich; Technion Israel Institute of Technology; University of Leeds
摘要：We construct and study a stationary version of the Hastings-Levitov(0) model. We prove that, unlike in the classical HL(0) model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL(0) is proposed as a potential candidate for a stationary off-lattice variant of diffusion limited aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finitenes...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dupuis, Paul; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; Iowa State University
摘要：Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n(2), where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is...
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作者：Cordero, Fernando; Hummel, Sebastian; Schertzer, Emmanuel
作者单位：University of Bielefeld; Sorbonne Universite; Universite Paris Cite
摘要：Lambda-Wright-Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate frequency-dependent selection. A decomposition of the drift allows us to approximate the solution of the stochastic differential equation by a sequence of Moran models. The genealogical structure underlying the Moran model leads in the large population limit to a gener...
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作者：Adler, Mark; Johansson, Kurt; van Moerbeke, Pierre
作者单位：Brandeis University; Royal Institute of Technology; Universite Catholique Louvain; Brandeis University
摘要：Random tilings of geometrical shapes with dominos or lozenges have been a rich source of universal statistical distributions. This paper deals with domino tilings of checker board rectangular shapes such that the top two and bottom two adjacent squares have the same orientation and the two most left and two most right ones as well. It forces these so-called skew-Aztec rectangles to have cuts on either side. For large sizes of the domain and upon an appropriate scaling of the location of the cu...
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作者：Lu, Jianfeng; Wang, Lihan
作者单位：Duke University; Duke University; Duke University
摘要：We establish L-2-exponential convergence rate for three popular piece-wise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincare-type inequality in time-augmented state space and a standard L-2 energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing r...
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作者：Nutz, Marcel; Wang, Ruodu
作者单位：Columbia University; University of Waterloo
摘要：We introduce a constrained optimal transport problem where origins x can only be transported to destinations y >= x. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect Y - X given marginals when the effect is monotone, or Y >= X. We thus focus on supermodular costs (or submodular rewards) and introduce a coupling P-* that is optimal for all such costs and yields the sharp bound. This coupling admits manifold characterizations-geometric, ord...
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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 extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test functions. We also obtain a continuous version of the multi-dimensional Wasserstein bound in terms of fourth moments. We apply the main results to multivariate normal approximations to Wishart matrices of size n and degree d, where we obtain the optimal con...
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作者：Collevecchio, Andrea; Tuan-Minh Nguyen; Volkov, Stanislav
作者单位：Monash University; Lund University
摘要：We consider a nonlinear vertex-reinforced jump process (VRJP(w)) on Z with an increasing measurable weight function w : [1, infinity) -> [1, infinity) and initial weights equal to one. Our main goal is to study the asymptotic behaviour of VRJP(w) depending on the integrability of the reciprocal of w. In particular, we prove that if integral(infinity)(1) du/w(u) = infinity then the process is recurrent, that is, it visits each vertex infinitely often and all local times are unbounded. On the ot...
