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作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a cluster growth model on Z(d), called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It is known that the asymptotic shape of the cluster is spherical. When dimension is 2 or more, we prove that fluctuations with respect to a sphere are at most a power of the logarithm of its radius in dimension d >= 2. In so doing, we introduce a closely rel...
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作者：Cheliotis, Dimitris; den Hollander, Frank
作者单位：National & Kapodistrian University of Athens; Leiden University - Excl LUMC; Leiden University
摘要：In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges.. There are two phases, localized and delocaliied, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process [Birkner, Greven and den Hollander, Probab. Theory Related Fields 148 (2010) 403-456], we derive va...
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作者：Friedli, S.; Ioffe, D.; Velenik, Y.
作者单位：Universidade Federal de Minas Gerais; Technion Israel Institute of Technology; University of Geneva
摘要：We consider the Bernoulli bond percolation process P-p,P-p' on the nearestneighbor edges of Z(d), which are open independently with probability p < p(c), except for those lying on the first coordinate axis, for which this probability is p'. Define xi(p,p') := - lim(n ->infinity) n(-1) log P-p,P-p' (0 <-> -ne(1)) and xi(p) := xi(p,p). We show that there exists p(c)' = p(c)'(p, d) such that xi(p,p)' = xi(p) if p' < p(c)' and xi(p,p)' < xi(p) if p' > p(c)'. Moreover, p(c)'(p, 2) = p(c)'(p, 3) = p...
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作者：Osada, Hirofumi
作者单位：Kyushu University
摘要：We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in R-d and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and act over a long range in nature. The associated equilibrium states are no longer Gibbs measures. We present general results for the construction of such diffusions and, as applications thereof, construct two typical interacting Brownian motions with logarithmic intera...
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作者：Da Prato, G.; Flandoli, F.; Priola, E.; Roeckner, M.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Turin; University of Bielefeld
摘要：We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on R-d to infinite dimensions. Because Sobolev regularity results implying continuity or smoothness of functions do not hold on infinite-dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The pric...
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作者：Conus, Daniel; Joseph, Mathew; Khoshnevisan, Davar
作者单位：Lehigh University; Utah System of Higher Education; University of Utah
摘要：We consider a nonlinear stochastic heat equation at partial derivative(t)u = 1/2 partial derivative(xx)u + sigma(u)partial derivative W-xt, where partial derivative(xt) W denotes space time white noise and sigma : R -> R is Lipschitz continuous. We establish that, at every fixed time t > 0, the global behavior of the solution depends in a critical manner on the structure of the initial function u(0): under suitable conditions on u(0) and sigma, sup(x is an element of R)u(t)(x) is a.s. finite w...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We prove an upper bound for the epsilon-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to T-RW(G) ln(vertical bar V vertical bar/epsilon), where vertical bar V vertical bar is the number of vertices in G, and T-RW(G) is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-...
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作者：Bayati, Mohsen; Gamarnik, David; Tetali, Prasad
作者单位：Stanford University; Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology
摘要：We establish the existence of free energy limits for several combinatorial models on Erdos-Renyi graph G(N, [cN]) and random r-regular graph G(N, r). For a variety of models, including independent sets, MAX-CUT, coloring and K-SAT, we prove that the free energy both at a positive and zero temperature, appropriately rescaled, converges to a limit as the size of the underlying graph diverges to infinity. In the zero temperature case, this is interpreted as the existence of the scaling limit for ...
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作者：Chen, Wei-Kuo
作者单位：University of California System; University of California Irvine
摘要：We consider a spin system obtained by coupling two distinct Sherrington-Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the overlap under the corresponding Gibbs measure is essentially concentrated at a single value. In the absence of external field, this statement was first confirmed by Chatterjee [Disorder chaos and multiple valleys in spin glasses (2009) Preprint]. In the prese...
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作者：del Barrio, Eustasio; Matran, Carlos
作者单位：Universidad de Valladolid
摘要：We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube [0, 1](d) and the true measure. This is a family of problems lying in between classical optimal transportation and nearest neighbor problems. We show that the empirical cost of optimal incomplete transportation vanishes at rate O-P(n(-1/d)), where n denotes the sample size. In dimension d >= 3 the rate is the same as in classical optimal transpor...
