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作者：Bie, ESL
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
摘要：We study a Stochastic Partial Differential Equation, of parabolic type, set on IRd, with d is an element of N. This equation is driven by a Poisson random measure, either compensated or not. The first part of this work shows existence and uniqueness of a progressively measurable solution. The technics involved are close to those used to deal with analogous equations driven by a Gaussian noise. The second part gives some criterions on the intensity of the Poisson random measure, in order to ens...
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作者：Zahle, M
作者单位：Friedrich Schiller University of Jena
摘要：The classical Lebesgue-Stieltjes integral integral(a)(b)f dg of real or complex-valued functions on a finite interval (a, b) is extended to a large class of integrands f and integrators g of unbounded variation. The key is to use composition formulas and integration-by-part rules for fractional integrals and Weyl derivatives. In the special case of Holder continuous functions f and g of summed order greater than 1 convergence of the corresponding Riemann-Stieltjes sums is proved. The results a...
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作者：Sun, YE
作者单位：National University of Singapore; Yale University
摘要：For a large collection of random variables in an ideal setting, pairwise independence is shown to be almost equivalent to mutual independence. An asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and asymptotic mutual independence for a triangular array (or a sequence) of random variables. Similar equivalence is also presented for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability. General...
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作者：Benjamini, I; Schramm, O
作者单位：Weizmann Institute of Science
摘要：Consider the standard continuous percolation in IR4, and choose the parameters so that the induced percolation on a fixed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.
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作者：Toth, B; Werner, W
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Universite Paris Saclay
摘要：We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density in the 'immediate neighbourhood' of the point it is just visiting. We focus on the most natural process with these properties that we call 'true self-repelling motion'. This is the continuous counterpart to the integer-valued 'true' self-avoiding walk, which had bee...
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作者：Toubol, A
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris Cite
摘要：Comets and Neveu have initiated in [5] a method to prove convergence of the partition function of disordered systems to a lognormal random variable in the high temperature regime by means of stochastic calculus. We generalize their approach to a multidimensional Sherrington-Kirkpatrick model with an application to the Heisenberg model of uniform spins on a sphere of R-d, see [9]. The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical en...
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作者：Cekanavicius, V
作者单位：Vilnius University
摘要：For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets. Asymptotics can be constructed two-ways: by adding summands to the leading term or by adding summands in its exponent. The choice of approximations is confirmed by the Ibragimov-type necessary and sufficient conditions.
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作者：Erdos, L
作者单位：New York University
摘要：We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrodinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Brezin, Gross and Itzykson which pre...
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作者：Pfister, CE; Velenik, Y
摘要：We study the 2D Ising model in a rectangular box Lambda(L) of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization Sigma(t is an element of Lambda L) sigma(t) when L --> infinity for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter m* is strictly positive. We study in particular boundary effects due to an arbitrary real-valued boundary magnetic field. Using the self-duality of th...
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作者：Kifer, Y
摘要：The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers e...
