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作者：Beckman, Erin; Cook, Keisha; Eikmeier, Nicole; Hernandez-Torres, Sarai; Junge, Matthew
作者单位：Concordia University - Canada; Tulane University; Grinnell College; Technion Israel Institute of Technology; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the variant in which red particles die and describe the phase diagram for the resulting process on infinite d-ary trees. A novel connection to weighted Catalan numbers makes it possible to characterize the critical behavior.
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作者：Krylov, N., V
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For the Ito stochastic equations in R-d with drift in L-d, several results are discussed, such as the existence of weak solutions, the existence of the corresponding Markov process, the Aleksandrov type estimates of their Green's functions, which yield their summability to the power of d/(d - 1), the Fabes-Stroock type estimates, which show that Green's functions are summable to a higher degree, the Fanghua Lin type estimates, which are one of the main tools in the W-p(2)-theory of fully nonli...
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作者：Dimitrov, Evgeni; Matetski, Konstantin
作者单位：Columbia University
摘要：In this paper we show that a Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its top curve, that is, the finite-dimensional sets of the top curve form a separating class. A particular consequence of our result is that the parabolic Airy line ensemble is the unique Brownian Gibbsian line ensemble, whose top curve is the parabolic Airy(2) process.
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作者：Rath, Balazs; Swart, Jan M.; Terpai, Tamas
作者单位：Budapest University of Technology & Economics; MTA-BME Stochastics Research Group; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Eotvos Lorand University
摘要：In frozen percolation, i.i.d. uniformly distributed activation times are assigned to the edges of a graph. At its assigned time an edge opens provided neither of its end vertices is part of an infinite open cluster; in the opposite case it freezes. Aldous (Math. Proc. Cambridge Philos. Soc. 128 (2000) 465477) showed that such a process can be constructed on the infinite 3-regular tree and asked whether the event that a given edge freezes is a measurable function of the activation times assigne...
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作者：Xu, Changji
作者单位：Harvard University
摘要：Consider the discrete cube {-1, 1}(N) and a random collection of half spaces which includes each half space H(x) := {y is an element of {-1, 1}(N) : x center dot y >=kappa root N} for x. {-1, 1}(N) independently with probability p. Is the intersection of these half spaces empty? This is called the Ising perceptron model under Bernoulli disorder. We prove that this event has a sharp threshold, that is, the probability that the intersection is empty increases quickly from is an element of to 1 -...
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作者：Chen, Xia; Deya, Aurelien; Ouyang, Cheng; Tindel, Samy
作者单位：University of Tennessee System; University of Tennessee Knoxville; Universite de Lorraine; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
摘要：The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: partial derivative(t)u(t) (x) = 1/2 Delta u(t) (x) + u(t) (x). (W) over dot (x), for t is an element of R+ and x is an element of R-d, where (W) over dot (x) is a Gaussian noise whose space time covariance function is singular. In this rough context we shall give some information about the moments of u(t) (x) when the stochastic heat equation is interpreted in the S...
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作者：Ahlberg, Daniel; Griffiths, Simon; Janson, Svante
作者单位：Stockholm University; Pontificia Universidade Catolica do Rio de Janeiro; Uppsala University
摘要：We study a model of competition between two types evolving as branching random walks on Z(d). The two types are represented by red and blue balls, respectively, with the rule that balls of different colour annihilate upon contact. We consider initial configurations in which the sites of Z(d) contain one ball each which are independently coloured red with probability p and blue otherwise. We address the question of fixation, referring to the sites and eventually settling for a given colour or n...
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作者：Dalang, Robert C.; Mueller, Carl; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Michigan State University
摘要：We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, x)(W) over dot (t, x). Here, t >= 0, x is an element of R and (W) over dot (t, x) is an R-d-valued space-time white noise. We say that a point z is an element of R-d is polar if P{u(t, x) = z for some t > 0 and x is an element of R} = 0. We ...
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
摘要：There is a slight gap and error in Remark 3.4 of Ann. Probab. 41, no. 5 (2013), 3284-3305, that was not noticed before the first errata were published (Ann. Probab. 46, no. 4 (2018), 2400-2405). We take this opportunity to provide some additional updates as well.
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作者：Addario-Berry, Louigi; Corsini, Benoit
作者单位：McGill University
摘要：Random binary search trees are obtained by recursively inserting the elements sigma(1), sigma(2),..., sigma(n) of a uniformly random permutation s of [n] = {1,..., n} into a binary search tree data structure. Devroye (J. Assoc. Comput. Mach. 33 (1986) 489-498) proved that the height of such trees is asymptotically of order c* log n, where c* = 4.311... is the unique solution of c log((2e)/c) = 1 with c >= 2. In this paper, we study the structure of binary search trees T-n,T- q built from Mallo...
