-
作者：Baake, Ellen; Cordero, Fernando; Hummel, Sebastian
作者单位：University of Bielefeld
摘要：We consider the mutation-selection differential equation with pairwise interaction (or, equivalently, the diploid mutation-selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph. The formal relation to the forward model is given via duality. To make the tree tractable, we prune branches upon mutations, thus reducing it to its informative parts. The hierarchies inherent in the tree are encoded systematically v...
-
作者：Banerjee, Sayan; Budhiraja, Amarjit; Puha, Amber L.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; California State University System; California State University San Marcos
摘要：We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. Since one needs to keep track of the remaining processing times of all jobs in the system in order to describe the evolution, a natural state descriptor for an SRPT queue is a measure valued process in which the state of the system at a given time is the finite nonnegative Borel measure...
-
作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
摘要：It was shown in (J. Amer. Math. Soc. 24 (2011) 919-944) that the edge of the spectrum of beta ensembles converges in the large N limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature 1/beta goes to infinity: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on R of intensity ex dx and that the eigenfunctions converge t...
-
作者：Chen, Hong-Bin
作者单位：New York University
摘要：We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of the two vectors are only assumed to have scaled bounded supports. We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the ...
-
作者：Chassagneux, Jean-Francois; Szpruch, Lukasz; Tse, Alvin
作者单位：Universite Paris Cite; University of Edinburgh
摘要：Consider the metric space (P-2(R-d), W-2) of square integrable laws on R-d with the topology induced by the 2-Wasserstein distance W-2. Let Phi : P-2(R-d) -> R and mu is an element of P-2(R-d). In this work, we consider (a) mu(N) being the empirical measure of N-samples from mu, and the other case in which (b) mu(N) is the empirical measure of marginal laws of the particle system of a McKean-Vlasov PDE (mu(t))(t). The main result of this paper is to show that under suitable regularity conditio...
-
作者：Bandyopadhyay, Antar; Thacker, Debleena
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; Durham University
摘要：In this work, we introduce a generalization of the classical Polya urn scheme (Ann. Inst. Henri Poincare 1 (1930) 117-161) with colors indexed by a Polish space, say, S. The urns are defined as finite measures on S endowed with the Borel sigma-algebra, say, S. The generalization is an extension of a model introduced earlier by Blackwell and MacQueen (Ann. Statist. 1 (1973) 353-355). We present a novel approach of representing the observed sequence of colors from such a scheme in terms an assoc...
-
作者：Borga, Jacopo; Cavalli, Benedetta
作者单位：University of Zurich
摘要：We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league accord-ing to independent ergodic processes. The result of each match is random: the probability that a team wins against another team is determined by a function of the strengths of the two teams in the day the match is played. Our model generalizes some previous models studi...
-
作者：Disanto, Filippo; Fuchs, Michael; Paningbatan, Ariel R.; Rosenberg, Noah A.
作者单位：University of Pisa; National Chengchi University; University of the Philippines System; University of the Philippines Diliman; Stanford University
摘要：For a pair consisting of a gene tree and a species tree, the ancestral con-figurations at a species-tree internal node are the distinct sets of gene lin-eages that can be present at that node. The enumeration of root ancestral configurations-ancestral configurations at the species-tree root-assists in describing the complexity of gene-tree probability calculations in evolution-ary biology. Assuming that the gene tree and species tree match in topology, we study the distribution of the number o...
-
作者：Adhikari, Kartick; Adler, Robert J.; Bobrowski, Omer; Rosenthal, Ron
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：In this paper we study the spectrum of the random geometric graph G(n, r), in a regime where the graph is dense and highly connected. In the Erdos-Renyi G(n, p) random graph it is well known that upon connectivity the spectrum of the normalized graph Laplacian is concentrated around 1. We show that such concentration does not occur in the G(n, r) case, even when the graph is dense and almost a complete graph. In particular, we show that the limiting spectral gap is strictly smaller than 1. In ...
-
作者：Ben Alaya, Mohamed; Kebaier, Ahmed; Ngo, Thi Bao Tram
作者单位：Universite de Rouen Normandie; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we give a natural extension of the antithetic multilevel Monte Carlo (MLMC) estimator for a multidimensional diffusion introduced by Giles and Szpruch (Ann. Appl. Probab. 24 (2014) 1585-1620) by considering the permutation between m Brownian increments, m >= 2, instead of using two increments as in the original paper. Our aim is to study the asymptotic behavior of the weak errors involved in this new algorithm. Among the obtained results, we prove that the error between on the o...
