ﻻ يوجد ملخص باللغة العربية
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):=-logintvarrho({d}kappa)expbiggl[-{1/2}kappaet a^2biggr],] where $varrho$ is a positive measure with compact support in $(0,infty)$. Hence, the potential $V$ is symmetric, but nonconvex in general. While for strictly convex $V$s, the translation-invariant, ergodic gradient Gibbs measures are completely characterized by their tilt, a nonconvex potential as above may lead to several ergodic gradient Gibbs measures with zero tilt. Still, every ergodic, zero-tilt gradient Gibbs measure for the potential $V$ above scales to a Gaussian free field.
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.:
We consider a class of interacting particle systems with values in $[0,8)^{zd}$, of which the binary contact path process is an example. For $d ge 3$ and under a certain square integrability condition on the total number of the particles, we prove a
We study a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control, and quadratic dependence on control of the cost function. For this class of problems we establish existence and uniqueness of an optimal contro
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $rho$ on $mathbb{Z}_-$ and $lambda$ on $mathbb{Z}_+$, and a second class particle initially at the origin. For $rho<lambda$, there is
We give the ``quenched scaling limit of Bouchauds trap model in ${dge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent $alpha$-stable subordinator.