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21.
This paper is devoted to a detailed study of a p-spins interaction model with external field, including some sharp bounds on the speed of self averaging of the overlap as well as a central limit theorem for its fluctuations, the thermodynamical limit for the free energy and the definition of an Almeida–Thouless type line. Those results show that the external field dominates the tendency to disorder induced by the increasing level of interaction between spins, and our system will share many of its features with the SK model, which is certainly not the case when the external magnetic field vanishes.  相似文献   
22.
Nualart  David  Tindel  Samy 《Potential Analysis》1997,7(3):661-680
In this note we prove a result of existence and uniqueness of solutions for a certain class of hyperbolic stochastic differential equations with additive white noise and nondecreasing coefficient. We then show the convergence of Euler's approximation scheme for this equation.  相似文献   
23.
We study nonlinear heat and wave equations on a Lie group. The noise is assumed to be a spatially homogeneous Wiener process. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.  相似文献   
24.
In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a fractional Brownian motion with Hurst parameter H>1/2H>1/2 and obtain some (functional) convergence properties of some empirical measures of the Euler scheme to the stationary solutions of such SDEs.  相似文献   
25.
This paper is concerned with two related types of directed polymers in a random medium. The first one is a d-dimensional Brownian motion living in a random environment which is white-noise in time and homogeneous in space. The second is a continuous-time discrete-space Markov process on ℤ d , in a random environment with similar properties as in continuous space, albeit defined only on . The case of a space-time white noise environment can be achieved in this second setting. By means of some Gaussian tools, we estimate the free energy of these models at low temperature, and give some further information on the strong disorder regime of the objects under consideration. Frederi Viens’ research partially supported by NSF grants no.: DMS 0204999 and DMS 0606615.  相似文献   
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