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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...
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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Roma Tre University
摘要：Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph G = (V, E) dual to the biased voter model on G. Our main goal is tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as vertical bar V vertical bar -> infinity. Our results allow...
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作者：Pain, Michel; Senizergues, Delphin
作者单位：New York University; University of British Columbia
摘要：Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of weights, the first order for the height of such trees has been recently established by one of the authors. In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions. Our met...
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作者：Bao, Zhigang; He, Yukun
作者单位：Hong Kong University of Science & Technology; City University of Hong Kong
摘要：Let FN and F be the empirical and limiting spectral distributions of an N x N Wigner matrix. The Cramer-von Mises (CvM) statistic is a classical goodness-of-fit statistic that characterizes the distance between FN and F in L2-norm. In this paper, we consider a mesoscopic approximation of the CvM statistic for Wigner matrices, and derive its limiting distribution. In the Appendix, we also give the limiting distribution of the CvM statistic (without approximation) for the toy model CUE.
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作者：Hill, Max; Legried, Brandon; Roch, Sebastien
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Michigan System; University of Michigan
摘要：We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as mod-eled by a coalescent process) and gene duplication and loss (as modeled by a branching process). Through a probabilistic analysis of the model, we derive sample complexity bounds for widely used quartet-based inference methods that highlight the effect of the duplication and loss rates in both subcritical and supercritical regimes.
