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作者：Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We consider a class of Gibbs measures defined with respect to increments {omega(t) - omega(s)}(s 0) and unbounded (singular) interactions (including singularities of the form x bar right arrow 1/vertical bar x vertical bar(p) in d >= 3 or x bar right arrow delta(0)(x) in d = 1) attached to the space variables. These assumptions on the interaction seem to be sharp and cover quantum mechanical models like the Nelson model and the polaron problem with ultraviolet cut off (both carrying bounded sp...
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作者：Bufetov, Alexey; Gorin, Vadim; Romik, Dan
作者单位：Leipzig University; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Davis
摘要：The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multispecies version of the totally asymmetric simple exclusion process (TASEP) on a finite interval. An open problem from a 2009 paper of Angel, Holroyd, and Romik asks for the limiting distribution of the absorbing time of the process as the number of particles goes to infinity. We resolve this question by proving that this random variable satisfies GOE Tracy-Widom asymptotics. As ...
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作者：Banerjee, Sayan; Olvera-Cravioto, Mariana
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of the model parameters. Interestingly, this power law is heavier than the tail of the limiting in-degree distribution, which goes against the commonly accepted power law hypothesis. This deviation from the power law hypothesis points at the structural difference...
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作者：Guo, Chengkun; Tang, Si; Wei, Ningxi
作者单位：Lehigh University
摘要：We study the recurrence property of one-per-site frog model FM(d, p) on a d-ary tree with drift parameter p is an element of [0, 1], which determines the bias of frogs' random walks. In this model, active frogs move toward the root with probability p or otherwise move to a uniformly chosen child vertex. Whenever a site is visited for the first time, a new active frog is introduced at the site. We are interested in the minimal drift p(d) so that the frog model is recurrent. Using a coupling arg...
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作者：Maillard, Pascal; Paquette, Elliot
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; McGill University
摘要：We consider a Markovian evolution on point processes, the psi -process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a new point is added uniformly within it. Building on previous work of the authors and of Junge, we show that the empirical distribution of points in such a process is always equidistributed under mild assumptions on the rule, generalizing work of Junge. A major ...
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作者：Burdzy, Krzysztof; Kolodziejek, Bartosz; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Warsaw University of Technology; Microsoft
摘要：We study solutions to the stochastic fixed-point equation X =(d) AX + B where the coefficients A and B are nonnegative random variables. We introduce the local dependence measure (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of X. We discuss the relationship of LDM with earlier results on the stochastic fixed-point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.
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作者：Helmuth, Tyler; Perkins, Will; Petti, Samantha
作者单位：Durham University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Harvard University
摘要：We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three and higher. As the dimension tends to infinity, our improvements are by factors of 2 and 1.7, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and te...
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作者：Kolokoltsov, Vassili N.
作者单位：University of Warwick
摘要：In this paper we are merging the two new branches of game theory: quantum games and mean-field games (MFG). Building a quantum analog of MFGs requires the full reconstruction of its foundations and methodology, because in N-particle quantum evolution particles are not separated in individual dynamics and the key concept of the classical MFG theory, the empirical measure defined as the sum of Dirac masses of the positions of the players, is not applicable in quantum setting. As a preliminary re...
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作者：Horst, Ulrich; Xu, Wei
作者单位：Humboldt University of Berlin; Humboldt University of Berlin
摘要：We provide a general probabilistic framework within which we estab-lish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Vari-ous well-studied stochastic volatility models wit...
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作者：Piatnitski, Andrey; Pirogov, Sergey; Zhizhina, Elena
作者单位：UiT The Arctic University of Tromso; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
摘要：The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating locally periodic coefficient and, under natural ellipticity and localization conditions, show that the family satisfies the large deviation principle in the path space equipped with Skorokhod topology. The corre-sponding rate function is defined in terms of a fa...
