We consider the asymmetric simple exclusion process (ASEP) on Z started from step initial data and obtain exact Lyapunov exponents for H0(t), integrated current of ASEP. As a corollary, we derive an explicit formula upper-tail large deviation rate function −H0(t). Our result matches with totally (TASEP) obtained in [40].

Let X k be a sequence of independent and identically distributed random variables taking values in a compact metric space , and consider the problem of estimating the law of X 1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequenc...

We use process level large deviation analysis to obtain the rate function for a general family of occupancy problems. Our interest is the asymptotics of the empirical distributions of various quantities (such as the fraction of urns that contain a given number of balls). In the general setting, balls are allowed to land in a given urn depending on the urn’s contents prior to the throw. We discu...