Local Limit Theorems for Lattice Random Variables

Equivalence of ensembles for two-species zero-range invariant measures

“…For ρ ∈ ∂ D ρ the same argument holds as long as ν 1 M(ρ) has finite covariance. If it does not, the same conclusion follows from convergence to an α-stable limit law with rate of convergence 1/L 2/α f (L), where α ∈ (0, 2) and f is slowly varying as L → ∞ (see [17,18] for multivariate local limit theorems in the non-Gaussian case). …”

On transition of distributions of sums of independent identically distributed random variables from one lattice to another in the generalised allocation scheme

“…Some of limit theorems proved in this paper and in [6] can likely be obtained by checking the general conditions for validity of local limit theorems given in [12] (see [3]), but the authors believe that the presence of simple direct proofs may be of advantage in future studies.…”

Asymptotics of the regression quantile basic solution under misspecification

“…For more information on conditions under which local limit theorems hold, see [16] and [17]. The typical scenario envisaged is one where the non-intercept component of µ has no lattice components and τ is rational.…”