A general central limit theorem and a subsampling variance estimator for α ‐mixing point processes

Local Central Limit Theorem for Determinantal Point Processes

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 Central Limit Theorem and a Strong Mixing Condition.

A Lyapunov type central limit theorem for mixing quantum systems

Physical systems, composed of interacting identical (or similar) subsystems appear in many branches of physics. They are standard in condensed matter physics. Assuming that each subsystem only interacts with its nearest neighbours and that the energy per subsystem has an upper limit, which must not depend on the number of subsystems n, we show that the distribution of energy eigenvalues of almo...

A Central Limit Theorem For Reversible Processes With Non-linear Growth of Variance∗

Kipnis and Varadhan showed that for an additive functional, Sn say, of a reversible Markov chain the condition E(S n)/n→ κ ∈ (0,∞) implies the convergence of the conditional distribution of Sn/ √ E(S2 n), given the starting point, to the standard normal distribution. We revisit this question under the weaker condition, E(S n) = n`(n), where ` is a slowly varying function. It is shown by example...

Central Limit Theorem for Stationary Linear Processes

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.