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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...
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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...
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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 ...
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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...
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作者：Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We consider a class of Gibbs measures defined with respect to increments {omega(t) - omega(s)}(s 0) and unbounded (singular) interactions (including singularities of the form x bar right arrow 1/vertical bar x vertical bar(p) in d >= 3 or x bar right arrow delta(0)(x) in d = 1) attached to the space variables. These assumptions on the interaction seem to be sharp and cover quantum mechanical models like the Nelson model and the polaron problem with ultraviolet cut off (both carrying bounded sp...
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作者：Bufetov, Alexey; Gorin, Vadim; Romik, Dan
作者单位：Leipzig University; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Davis
摘要：The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multispecies version of the totally asymmetric simple exclusion process (TASEP) on a finite interval. An open problem from a 2009 paper of Angel, Holroyd, and Romik asks for the limiting distribution of the absorbing time of the process as the number of particles goes to infinity. We resolve this question by proving that this random variable satisfies GOE Tracy-Widom asymptotics. As ...
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作者：Banerjee, Sayan; Olvera-Cravioto, Mariana
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of the model parameters. Interestingly, this power law is heavier than the tail of the limiting in-degree distribution, which goes against the commonly accepted power law hypothesis. This deviation from the power law hypothesis points at the structural difference...
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作者：Guo, Chengkun; Tang, Si; Wei, Ningxi
作者单位：Lehigh University
摘要：We study the recurrence property of one-per-site frog model FM(d, p) on a d-ary tree with drift parameter p is an element of [0, 1], which determines the bias of frogs' random walks. In this model, active frogs move toward the root with probability p or otherwise move to a uniformly chosen child vertex. Whenever a site is visited for the first time, a new active frog is introduced at the site. We are interested in the minimal drift p(d) so that the frog model is recurrent. Using a coupling arg...
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作者：Maillard, Pascal; Paquette, Elliot
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; McGill University
摘要：We consider a Markovian evolution on point processes, the psi -process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a new point is added uniformly within it. Building on previous work of the authors and of Junge, we show that the empirical distribution of points in such a process is always equidistributed under mild assumptions on the rule, generalizing work of Junge. A major ...
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作者：Burdzy, Krzysztof; Kolodziejek, Bartosz; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Warsaw University of Technology; Microsoft
摘要：We study solutions to the stochastic fixed-point equation X =(d) AX + B where the coefficients A and B are nonnegative random variables. We introduce the local dependence measure (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of X. We discuss the relationship of LDM with earlier results on the stochastic fixed-point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.
