作者：Jara, Milton; Menezes, Otavio
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidade de Lisboa
摘要：We establish an invariance principle for a one-dimensional random walk in a dynamic random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes: a Brownian motion and a Gaussian process with stationary increments.
作者：Bates, Erik; Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley; Stanford University
摘要：For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain: (i) a version of complete path localization for directed polymers that is not available even for exactly solvable models, and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities.
