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作者：Athreya, Siva; den Hollander, Frank; Rollin, Adrian
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Leiden University; Leiden University - Excl LUMC; National University of Singapore
摘要：The goal of this paper is to construct a natural class of graphon-valued processes arising from population genetics. We consider finite populations where individuals carry one of finitely many genetic types and change type according to Fisher-Wright resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current types of the two individuals and on the current empirical type distribution of ...
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作者：Janson, Svante; Warnke, Lutz
作者单位：Uppsala University; University System of Georgia; Georgia Institute of Technology
摘要：We study the following preferential attachment variant of the classical Erd os-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly proportional to the product of the current degrees of its endpoints (note that the vertex set is fixed). We determine the asymptotic size of the giant component in the supercritical phase, confirming a conjecture of Pittel from 2010. Our proof uses a simple ...
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作者：Bielecki, Tomasz R.; Jakubowski, Jacek; Jeanblanc, Monique; Nieweglowski, Mariusz
作者单位：Illinois Institute of Technology; University of Warsaw; Universite Paris Saclay; Warsaw University of Technology
摘要：We consider a complete probability space (Omega, F, P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F subset of G. On this probability space we consider a real valued Gsemimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compu...
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作者：McVinish, Ross; Hodgkinson, Liam
作者单位：University of Queensland
摘要：Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we propose a new method for approximate simulation of spin systems which approximates the evolution of spin at each site between sampling epochs as an independent two-state Markov chain. Whe...
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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 obtain explicit error bounds for the d-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a nonlinear statistic of independent random variables or a sum of n locally dependent random vectors. We assume the approximating normal distribution has a nonsingular covariance matrix. The error bounds vanish even when the dimension d is much larger than the sample size n. We prove our main results using the ...
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作者：Chen, Xin; Kumagai, Takashi; Wang, Jian
作者单位：Shanghai Jiao Tong University; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：We study the quenched invariance principle for random conductance models with long range jumps on Z(d), where the transition probability from x to y is, on average, comparable to vertical bar x - y vertical bar(-(d+alpha)) with alpha is an element of (0, 2) but is allowed to be degenerate. Under some moment conditions on the conductance, we prove that the scaling limit of the Markov process is a symmetric alpha-stable Levy process on R-d. The well-known corrector method in homogenization theor...
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作者：Chleboun, Paul; Smith, Aaron
作者单位：University of Warwick; University of Ottawa
摘要：Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in ( J. Stat. Phys. 169 (2017) 441-471). Our main result is that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff...
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作者：Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein
作者单位：University of Bielefeld; Imperial College London; University of Agder
摘要：We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Mor...
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作者：Davies, Sami; Racz, Miklos Z.; Rashtchian, Cyrus
作者单位：University of Washington; University of Washington Seattle; Princeton University; University of California System; University of California San Diego
摘要：We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which req...
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作者：Mitsche, Dieter; Penrose, Mathew D.
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Bath
摘要：In the random geometric graph G(n, r(n)), n vertices are placed randomly in Euclidean d-space and edges are added between any pair of vertices distant at most r(n) from each other. We establish strong laws of large numbers (LLNs) for a large class of graph parameters, evaluated for G(n, r(n)) in the thermodynamic limit with nr(n)(d) = const., and also in the dense limit with nr(n)(d) -> infinity, r(n) -> 0. Examples include domination number, independence number, clique-covering number, eterna...
