ATYPICAL BEHAVIORS OF A TAGGED PARTICLE IN ASYMMETRIC SIMPLE EXCLUSION

Consider the asymmetric nearest-neighbor exclusion process (ASEP) on (Formula presented) with single particle drift γ > 0, starting from a Bernoulli product invariant measure ν_ρ with density ρ. It is known that the position X_N of a tagged particle, say initially at the origin, at time N satisfies an a.s. law of large numbers (Formula presented) as N ↑ ∞. In this context, we study the “typical” behavior of the tagged particle and “bulk” density evolution subject to “atypical” events {X_N ≥ AN} or {X_N ≤ AN} for A ≠ γ (1 − ρ). We detail different structures, depending on whether A < 0, 0 ≤ A < γ (1 − ρ), γ (1 − ρ) < A < γ or A ≥ γ, under which these atypical events are achieved, and compute associated large deviation costs. Among our results is an “upper tail” large deviation principle in scale N for (Formula presented).