Central Limit Theorem for Products of Random Matrices

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Central and Local Limit Theories in Markov Dependent Random Variables

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Central limit theorem for Z d + - actions by toral endomorphisms

In this paper we prove the central limit theorem for the following multisequence N1 ∑ n1=1 ... Nd ∑ nd=1 f(A1 1 ...A nd d x) where f is a Hölder’s continue function, A1, ..., Ad are s× s partially hyperbolic commuting integer matrices, and x is a uniformly distributed random variable in [0, 1]. Then we prove the functional central limit theorem, and the almost sure central limit theorem. The ma...

Notes on Free Probability Theory

Lecture 1. Free Independence and Free Harmonic Analysis. 2 1.1. Probability spaces. 2 1.2. Non-commutative probability spaces. 3 1.3. Classical independence. 4 1.4. Free products of non-commutative probability spaces. 5 1.5. Free Fock space. 6 1.6. Free Central Limit Theorem. 8 1.7. Free Harmonic Analysis. 10 1.8. Further topics. 16 Lecture 2. Random Matrices and Free Probability. 17 2.1. Rando...