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We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.
We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We s
We consider gradient fields $(phi_x:xin mathbb{Z}^d)$ whose law takes the Gibbs--Boltzmann form $Z^{-1}exp{-sum_{< x,y>}V(phi_y-phi_x)}$, where the sum runs over nearest neighbors. We assume that the potential $V$ admits the representation [V(eta):=-
We introduce a system of coalescing random paths with radialbehavior in a subsetof the plane. We call it theDiscrete Radial Poissonian Web. We show that underdiffusive scaling this family converges in distribution toa mapping of a restrictionof the Brownian Web.
We introduce trap models on a finite volume $k$-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [Nagahata, Y., Yoshida, N.: