. PR ] 1 3 A ug 1 99 9 Central Limit Theorem for Local Linear Statistics in Classical Compact Groups and Related Combinatorial Identities

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...

0 D ec 1 99 9 Q - multilinear Algebra

The Cayley-Hamilton-Newton theorem which underlies the Newton identities and the Cayley-Hamilton identity is reviewed, first, for the classical matrices with commuting entries, second, for two q-matrix algebras, the RTTalgebra and the RLRL-algebra. The Cayley-Hamilton-Newton identities for these q-algebras are related by the factorization map. A class of algebras M(R̂, F̂ ) is presented. The alge...

3 v 1 1 A pr 1 99 8 Fluctuation , time - correlation function and geometric Phase

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the “fast” system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation bet...

ar X iv : 1 10 9 . 32 20 v 1 [ m at h . PR ] 1 4 Se p 20 11 A limit theorem for occupation measures of Lévy processes in compact groups

A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.