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作者：Fan, Wai-Tong Louis; Legried, Brandon; ROCH, Sesbastien
作者单位：Indiana University System; Indiana University Bloomington; University of Michigan System; University of Michigan; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed k no statistically consistent phylogeny estimation is possible from k-mer counts over the full leaf sequences alone. Formally, we establish that the joint distribution of k-mer counts over the entire leaf sequences on two distinct trees have total variation distance bounded away from 1 as ...
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作者：Mueller, Carl; Neuman, Eyal
作者单位：University of Rochester; Imperial College London
摘要：We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in (0, infinity). Our main result states that the effective radius of the polymer is approximately J5/3; evidently for large J the polymer undergoes stretching. This contrasts with the equilibrium sit-uation without the time variable, where many earlier results show that the effective radius is approximately J.For such a moving polymer taking values in R2, we offer a conjecture that the eff...
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作者：Lacoin, Hubert; Yang, Shangjie
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study the dynamical behavior of a one dimensional interface interacting with a sticky impenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contacts between the interface and the substrate are given an energetic bonus while an external force with constant intensity pulls the interface away from the wall. Our interface is modeled by the graph of a one-dimensional nearest-neighbor path on Z(+), starting at 0 and ending at 0 after 2N steps, with ...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dewaskar, Miheer
作者单位：University of North Carolina; University of North Carolina Greensboro; Duke University
摘要：We consider the supermarket model in the usual Markovian setting where jobs arrive at rate n.n for some lambda(n) > 0, with n parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest among d(n) <= n randomly selected service queues. We show that when d(n) -> infinity and lambda(n) -> lambda is an element of (0,infinity), under natural conditions on the initial queues, the state occupancy process converges in probability, in a suitable path space, to the ...
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作者：Bernou, Armand; Fournier, Nicolas
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87-107) and (Comm. Math. Phys. 318 (2013) 375-409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension...
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作者：Fan, Zhou; Johnstone, Iain M.
作者单位：Yale University; Stanford University
摘要：We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the sup...
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作者：Amendola, Carlos; Klueppelberg, Claudia; Lauritzen, Steffen; Tran, Ngoc M.
作者单位：Technical University of Munich; University of Copenhagen; University of Texas System; University of Texas Austin
摘要：Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for Bayesian networks are far from exhausting valid conditional independence statements. We use tropical linear algebra to derive a compact representation of the conditional distribution given a partial observation, and exploit this to obtain a complete description of ...
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作者：Clark, Jeremy Thane
作者单位：University of Mississippi
摘要：We construct and study a family of random continuum polymer mea-sures Mr corresponding to limiting partition function laws recently derived in a weak-coupling regime for polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval [0, 1] into a compact diamond fractal having Hausdorff dimension two, and there is a natural uniform probability measure, mu, over t...
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作者：Hu, Yue; Dong, Jing; Perry, Ohad
作者单位：Columbia University; Northwestern University
摘要：We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers (queues) according to a pre-specified order, assuming that the switchover times between the queues are large relative to the processing times of individual jobs. Due to its complexity, computing an optimal control for such a system is prohibitive, and so we in...
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作者：Forman, Noah; Rizzolo, Douglas; Shi, Quan; Winkel, Matthias
作者单位：McMaster University; University of Delaware; University of Mannheim; University of Oxford
摘要：We give a pathwise construction of a two-parameter family of purelyatomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet(alpha,theta) distributions, for alpha is an element of(0, 1) and theta >= 0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields 148 (2010) 501-525). We build on our previous work on (alpha, 0)- and (alpha, alpha)-interval partition evolutions. The extension to general theta >= 0 is achieved...
