Dr. Rohini Kumar (UCSB)

Title: Current fluctuations for independent random walks

Abstract: In a system of independent and identical random walks, the hydrodynamic limit of particle density satisfies the transport pde. The
characteristics of this transport pde are straight lines with slope 'v', where 'v' is the mean velocity of the random walks. We will look at fluctuations of the particle current across characteristics. These fluctuations are subdiffusive. In the one-dimensional random walk model we construct a two-parameter current process indexed by time and spatial shifts in the characteristic line. The limiting scaled current process is found to be a mean-zero, two-parameter Gaussian process with given covariance. We define a distribution-valued current process for the random walk model in multiple dimensions and show that it's scaled limit is a distribution-valued Gaussian process with given covariance. Some large deviation results for the current process in the one-dimensional case will be presented.