, Cosmology Building, NTU
(臺灣大學次震宇宙館 )
Random Walk in Cooling Random Environment IV
Yiku Chino (National Yang Ming Chiao Tung University)
Abstract
The random walk in random environment (RWRE) is one of the classical models to describe the behavior of some object in a solvent with impurities. The model shows different asymptotic behavior depending on the moment condition for some parameter. The model on one dimensional lattice is solvable, but there remains a lot of open problems for the case in higher dimensions. In one dimension, Solomon showed the law of large numbers for the transient regime. Kesten, Kozlov and Spitzer proved the fluctuations for the transient regime and Sinai and Kesten proved for recurrent regime. The large deviation principle was also proved for both quenched and annealed cases. In this talk we consider a modification of RWRE, which is an intermediate model between RWRE and random walk in dynamical random environment (RWDRE) resetting the environment every unit of time. The model shows a crossover along the choice of how to reset the environment. To be precise, we define a deterministic sequence of times and re-sample the random environment at each time. We will see how much RWCRE is different from RWRE with some examples.