We prove a local central limit theorem (LCLT) for the number of points N(J) in a region J in Rd specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of N(J) tends to infinity as |J | → ∞. This extends a previous result giving a weaker central limit theorem (CLT) for these systems. Our result relies on the fact that the Lee-Yang zeros of t...

A local limit theorem is proved for partial sums of a hidden Markov chain, assuming global asymptotic normality for a related sum, a fairly weak mixing condition, and a non-lattice condition. The proof proceeds by a study of the conditional characteristic functions, the analysis of which relies heavily on a theorem from Breiman (1968). The paper concludes with a Cesaro type limit theorem for th...

We consider the limit distribution of the orders of the k largest components in the Erdős-Rényi random graph inside the “critical window” for arbitrary k. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems — yielding a Gaussian density multiplied by a highly oscillatory modulating factor — for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uni...

A version of central limit is established normalized sums dependent random when a theorem is and conditional are sufficiently The proof ideas from by representing density as integral of score function a translation of distributions. 1980 Subject 60F99.

We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a system are strictly less than 1. This extends the approach of [KL06] where the ordinary transfer operator was studied. 1. Results This paper deals with the issue...

We consider the continuous time version of the 'true' or 'myopic' self-avoiding random walk with site repulsion in 1d. The Ray – Knight-type method which was applied in [15] to the discrete time and edge repulsion case, is applicable to this model with some modifications. We present a limit theorem for the local time of the walk and a local limit theorem for the displacement.