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作者：Fribergh, Alexander; Kious, Daniel
作者单位：Universite de Montreal; New York University; NYU Shanghai
摘要：We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional law of large numbers for the position of the walker, properly rescaled. Moreover, we state a functional central limit theorem where an atypical process, related to the fractional kinetics, appears in the limit.
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作者：Hairer, Martin; Iyer, Gautam; Koralov, Leonid; Novikov, Alexei; Pajor-Gyulai, Zsolt
作者单位：University of Warwick; Carnegie Mellon University; University System of Maryland; University of Maryland College Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; New York University
摘要：This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: a Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging pri...
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作者：Martinsson, Anders
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We consider first-passage percolation on the class of high-dimensional graphs that can be written as an iterated Cartesian product G square G square...square G of some base graph G as the number of factors tends to infinity. We propose a natural asymptotic lower bound on the first-passage time between (v, v,...,v) and (w, w,...,w) as n, the number of factors, tends to infinity, which we call the critical time t(G)*(v,w). Our main result characterizes when this lower bound is sharp as n ->infin...
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作者：Panchenko, Dmitry
作者单位：University of Toronto
摘要：Using the synchronization mechanism developed in the previous work on the Potts spin glass model, we obtain the analogue of the Parisi formula for the free energy in the mixed even p-spin models with vector spins, which include the Sherrington-Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand's upper bound for the free energy of multiple mixed p-spin systems coupled by constraining their overlaps.
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作者：Bufetov, Alexander I.
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University
摘要：The main result of this paper is that determinantal point processes on R corresponding to projection operators with integrable kernels are quasiinvariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon-Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to t...
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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then apply this algorithm to study the WUSF, showing that every component of the WUSF is one-ended almost surely in any graph satisfying a certain weak anchored isoperimetric condition, that the number of 'excessive ends' in the WUSF is nonrandom in a...
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作者：Panchenko, Dmitry
作者单位：University of Toronto
摘要：We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational formula for the free energy, with the order parameter now given by a monotone path in the set of positive-semidefinite matrices. The main idea of the paper is a novel synchronization mechanism for blocks of overlaps. This mechanism can be used to ...
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作者：Pal, Soumik; Wong, Ting-Kam Leonard
作者单位：University of Washington; University of Washington Seattle; University of Southern California
摘要：A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper, we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximation than those of ordinary concave functions. The approximation error, called L-divergence, is different from the usual Bregman divergence. Using tools of information geometry a...
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作者：Kolli, Praveen; Shkolnikov, Mykhaylo
作者单位：Carnegie Mellon University; Princeton University
摘要：We consider systems of diffusion processes (particles) interacting through their ranks (also referred to as rank-based models in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to the solution of a linear parabolic SPDE with additive noise. The coefficients in the limiting SPDE are determined by the hydrodynamic limit of the particle system which, in turn, can ...
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作者：Kraaij, Richard C.
作者单位：Ruhr University Bochum
摘要：We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the generator of the Feller process, we are able to define a notion of absolutely continuous trajectories of measures in terms of some topology on this core. Also, we define a Hamiltonian in terms of the linear generator and a Lagrangian as its Legendre transfor...
