The Dobrushin-Hryniv Theory for the Two-Dimensional Lattice Widom-Rowlinson Model

Analytical Valuation of Contingent Claims by Stochastic Interacting Systems for Stock Market

“…where nv ⎡ ⎤ ⎢ ⎥ denote the integral part of a real number nv , and is a random variable which denote the area under the stock price. More specifically, for type-1 investors, considering the random walk (see [4,17,18]), and for a fixed , let…”

“…In this paper, we only consider the case that the 'area' is positive, and we can use the similar methods to discuss the opposite case. In the following, on some condition (see [4,17,18]), the limiting probability distribution of the random process…”

“…is given. The following results are based on the work of[1,3,4,10,17,18], that is, when β is large enough, the finite dimensional distribution of the conditional random process 1 converges to the corresponding distribution of random process…”

On an invariance principle for phase separation lines☆

“…Very low temperature cluster expansion based approach to a study of phase separation lines culminated in a series of works [12,[9][10][11][16][17][18]. In these works fluctuations of phase separation lines have been investigated for Ising, Blume-Capel and lattice Widom-Rowlinson interfaces.…”

Stochastic Interface Models

“…See Higuchi et al [146] for the extension to the two dimensional lattice Widom-Rowlinson model. [150,151], Ioffe and Schonmann [152] extended this result for all T < T c applying the method of percolation.…”