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作者：Antunovic, Tonci; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Texas A&M University System; Texas A&M University College Station
摘要：We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form G x z(+), where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in partic...
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作者：Franco, Tertuliano; Neumann, Adriana
作者单位：Universidade Federal da Bahia; Universidade Federal do Rio Grande do Sul
摘要：We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N-1, where N is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynam...
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作者：Dereich, Steffen; Mailler, Cecile; Morters, Peter
作者单位：University of Munster; University of Bath
摘要：We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same family, sharing the fitness of their parent, or be founders of new families, with a fitness sampled from a fitness distribution mu. Examples that can be embedded in this class are stochastic house-of-cards models, urn models with reinforcement and the preferenti...
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作者：Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
作者单位：University of Warwick; University of Geneva; University of Edinburgh
摘要：We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension d. The improved complexity is O(d(1/5)) compared to the complexity O(d(1/3)) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical va...
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作者：Heydenreich, Markus; Hulshof, Tim; Jorritsma, Joost
作者单位：University of Munich; Eindhoven University of Technology
摘要：Scale-free percolation is a percolation model on Z(d) which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience versus recurrence for dimension 1 and 2 and give sufficient conditions for transience in dimension 3 and higher. Finally, we show the existence of a hierarchical structure for parameters where vertices have degrees with infinite variance and obtain bounds on the cluster d...
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作者：Matzinger, Heinrich; Pachon, Angelica; Popov, Serguei
作者单位：University System of Georgia; Georgia Institute of Technology; University of Turin; Universidade Estadual de Campinas
摘要：We consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it observes. We show that up to equivalence the scenery can be reconstructed a.s. from the color record of all particles. To do so, we assume that the scenery has at least 2d + 1 colors which are i.i.d. with uniform probability. This is an improvement in comparison to Popov and Pachon [Stochastics 83 (2011) 107-116], where at each time the particles n...
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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：Given an instance of the preferential attachment graph G(n) = ([n], E-n), we would like to find vertex 1, using only local information about the graph; that is, by exploring the neighborhoods of small sets of vertices. Borgs et al. gave an algorithm which runs in time O(log(4) n), which is local in the sense that at each step, it needs only to search the neighborhood of a set of vertices of size O(log(4) n). We give an algorithm to find vertex 1, which w.h.p. runs in time O (omega log n) and w...
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作者：Baar, Martina; Bovier, Anton; Champagnat, Nicolas
作者单位：University of Bonn; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a model for Darwinian evolution in an asexual population with a large but nonconstant populations size characterized by a natural birth rate, a logistic death rate modeling competition and a probability of mutation at each birth event. In the present paper, we study the long-term behavior of the system in the limit of large population (K -> infinity) size, rare mutations (u -> 0) and small mutational effects (sigma -> 0), proving convergence to the canonical equation of adaptive dy...
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作者：Fricker, Christine; Tibi, Danielle
作者单位：Universite Paris Cite
摘要：For a class of large closed Jackson networks submitted to capacity constraints, asymptotic independence of the nodes in normal traffic phase is proved at stationarity under mild assumptions, using a local limit theorem. The limiting distributions of the queues are explicit. In the Statistical Mechanics terminology, the equivalence of ensembles-canonical and grand canonical-is proved for specific marginals. The framework includes the case of networks with two types of nodes: single server/finit...
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作者：van den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study a percolation model on the square lattice, where clusters freeze (stop growing) as soon as their volume (i.e., the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in van den Berg, de Lima and Nolin [Random Structures Algorithms 40 (2012) 220-226] and Kiss [Probab. Theory Related Fields 163 (2015) 713-768]. Using volume as a way to measure the size of a cluster instead of diamete...
