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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：In the Diffusion Limited Aggregation (DLA) process on Z(2), or more generally Z(d), particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}(n), in which particles take random decreasing walks from (1, ... , 1), and stick at the last vertex before the...
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作者：Loeper, Gregoire
作者单位：Monash University; Monash University
摘要：We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a nonlinear Black-Scholes equation that provides an exact replication strategy. This equation is fully nonlinear and singular, but we show that it is well posed, and we prove existence of smooth solutions for a large class of final payoffs, both for constant and local volatility. To obtain regularity of the solutions, we develop an original method based on Legendr...
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作者：Battiston, Marco; Favaro, Stefano; Roy, Daniel M.; Teh, Yee Whye
作者单位：University of Oxford; University of Turin; University of Toronto; Collegio Carlo Alberto
摘要：We characterize the class of exchangeable feature allocations assigning probability V-n,V-k Pi(l=1 WmlUn-ml)-W-k to a feature allocation of n individuals, displaying k features with counts (m(1), . . . ,m(k)) for these features. Each element of this class is parametrized by a countable matrix V and two sequences U and W of nonnegative weights. Moreover, a consistency condition is imposed to guarantee that the distribution for feature allocations of (n - 1) individuals is recovered from that of...
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作者：Chhita, S.; Ferrari, P. L.; Spohn, H.
作者单位：Durham University; University of Bonn; Technical University of Munich
摘要：For stationary KPZ growth in 1 + 1 dimensions, the height fluctuations are governed by the Baik-Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the diffusion coefficient of the initial conditions. The distributions are defined through a variational formula. We...
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作者：Angel, Omer; Kolesnik, Brett
作者单位：University of British Columbia; University of California System; University of California Berkeley
摘要：For fixed r >= 2, we consider bootstrap percolation with threshold r on the Erdos-Renyi graph G(n,p). We identify a threshold for p above which there is with high probability a set of size r that can infect the entire graph. This improves a result of Feige, Krivelevich and Reichman, which gives bounds for this threshold, up to multiplicative constants. As an application of our results, we obtain an upper bound for the threshold for K-4-percolation on G(n,p), as studied by Balogh, Bollobas and ...
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作者：Budhiraja, Amarjit; Friedlander, Eric
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider a rate control problem for an N-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state simultaneously. Such models have been proposed for large communication systems (e.g., ad hoc wireless networks) but are also suitable for other settings such as chemical-reaction networks. An associated diffusion control problem is presented and we show that the value func...
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作者：Benaim, Michel; Cloez, Bertrand; Panloup, Fabien
作者单位：Institut Agro; Montpellier SupAgro; Universite de Montpellier; INRAE; Universite d'Angers
摘要：As a continuation of a recent paper, dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ...
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作者：Duchamps, Jean-Jil; Lambert, Amaury
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Institut National de la Sante et de la Recherche Medicale (Inserm); Centre National de la Recherche Scientifique (CNRS); Universite PSL; College de France
摘要：Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure (infinitely-many-allele model) on the skeleton of the tree. The partition of the boundary into distinct alleles is the so-called allelic partition. In this paper, we are interested in the infinite trees generated by supercritical, possibly time-inhomogeneous, binary branching pr...
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作者：Leon, Jose R.; Samson, Adeline
作者单位：Universidad de la Republica, Uruguay; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; University of Central Venezuela
摘要：The FitzHugh-Nagumo is a well-known neuronal model that describes the generation of spikes at the intracellular level. We study a stochastic version of the model from a probabilistic point of view. The hypoellipticity is proved, as well as the existence and uniqueness of the stationary distribution. The bi-dimensional stochastic process is beta-mixing. The stationary density can be estimated with an adaptive non-parametric estimator. Then we focus on the distribution of the length between succ...
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作者：van der Hoorn, Pim; Olvera-Cravioto, Mariana
作者单位：Northeastern University; University of California System; University of California Berkeley
摘要：We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the in-degree and out-degree is finite, we show that the distance grows logarithmically in the size of the graph. In contrast with the undirected case, this can happen even when the variance of the degrees is infinite. The main tool in the analysis is a new coupling b...
