-
作者：Mueller, Marvin S.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Moving boundary problems allow to model systems with phase transition at an inner boundary. Motivated by problems in economics and finance, we set up a price-time continuous model for the limit order book and consider a stochastic and nonlinear extension of the classical Stefan-problem in one space dimension. Here, the paths of the moving interface might have unbounded variation, which introduces additional challenges in the analysis. Working on the distribution space, the Ito-Wentzell formula...
-
作者：Bernardin, Cedric; Goncalves, Patricia; Jara, Milton
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universidade de Lisboa
摘要：We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant, energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric Levy process. For a critical value of the coupling, the energy diffusion is described by a family of Levy processes which interpolate between these two processes.
-
作者：Swart, Jan M.
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching or...
-
作者：Thacker, Debleena; Volkov, Stanislav
作者单位：Lund University
摘要：Start with a graph with a subset of vertices called the border. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number xi of particles to be released by this final moment. We show...
-
作者：Biskup, Marek; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Charles University Prague; Texas A&M University System; Texas A&M University College Station
摘要：We study paths of time-length t of a continuous-time random walk on Z(2) subject to self-interaction that depends on the geometry of the walk range and a collection of random, uniformly positive and finite edge weights. The interaction enters through a Gibbs weight at inverse temperature beta; the energy is the total sum of the edge weights for edges on the outer boundary of the range. For edge weights sampled from a translation-invariant, ergodic law, we prove that the range boundary condensa...
-
作者：Damron, Michael; Hanson, Jack; Lam, Wai-Kit
作者单位：University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY); Indiana University System; Indiana University Bloomington
摘要：First-passage percolation is a random growth model defined using i.i.d. edge-weights (t(e)) on the nearest-neighbor edges of Z(d). An initial infection occupies the origin and spreads along the edges, taking time t(e) to cross the edge e. In this paper, we study the size of the boundary of the infected (wet) region at time t, B(t). It is known that B(t) grows linearly, so its boundary partial derivative B(t) has size between ct(d-1) and Ct(d). Under a weak moment condition on the weights, we s...
-
作者：Kiwi, Marcos; Mitsche, Dieter
作者单位：Universidad de Chile; Universidad de Chile; Universite Cote d'Azur
摘要：Random hyperbolic graphs have been suggested as a promising model of social networks. A few of their fundamental parameters have been studied. However, none of them concerns their spectra. We consider the random hyperbolic graph model, as formalized by [Automata, Languages, and Programming-39th International Colloquium-ICALP Part II. (2012) 573-585 Springer], and essentially determine the spectral gap of their normalized Laplacian. Specifically, we establish that with high probability the seco...
-
作者：Louart, Cosme; Liao, Zhenyu; Couillet, Romain
作者单位：Universite Paris Saclay
摘要：This article studies the Gram random matrix model G = 1/T Sigma E-T E = sigma (WX), classically found in the analysis of random feature maps and random neural networks, where X = [x(1),, x(T)] epsilon R-PXT is a (data) matrix of bounded norm, W epsilon R-nxp) is a matrix of independent zero-mean unit variance entries and o : R -> R is a Lipschitz continuous (activation) function-sigma (WX) being understood entry-wise. By means of a key concentration of measure lemma arising from nonasymptotic ...
-
作者：Giacomin, Giambattista; Lacoin, Hubert
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider the lattice Gaussian free field in d + 1 dimensions, d = 3 or larger, on a large box (linear size N) with boundary conditions zero. On this field, two potentials are acting: one, that models the presence of a wall, penalizes the field when it enters the lower half space and one, the pinning potential, rewards visits to the proximity of the wall. The wall can be soft, that is, the field has a finite penalty to enter the lower half-plane, or hard, when the penalty is infinite. In gen...
-
作者：Hening, Alexandru; Nguyen, Dang H.
作者单位：Tufts University; Wayne State University
摘要：In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n populations that live in a stochastic environment and which can interact nonlinearly (through com...
