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The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...

A Local Limit Theorem for Attraction to the Standard Normal Law: The Case of Infinitive Variance.

S.K. Basu (1984)

Metrika

A local limit theorem for directed polymers in random media : the continuous and the discrete case

Vincent Vargas (2006)

Annales de l'I.H.P. Probabilités et statistiques

A local limit theorem for the critical random graph.

Van Der Hofstad, Remco W., Kager, Wouter, Müller, Tobias (2009)

Electronic Communications in Probability [electronic only]

A local limit theorem on the semi-direct product of $ℝ^{* +}$ and $ℝ^{d}$

Émile Le Page, Marc Peigné (1997)

Annales de l'I.H.P. Probabilités et statistiques

A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs

Viviane Baladi, Aïcha Hachemi (2008)

Annales de l'I.H.P. Probabilités et statistiques

For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....

A log-scale limit theorem for one-dimensional random walks in random environments.

Roitershtein, Alexander (2005)

Electronic Communications in Probability [electronic only]

A Markov process underlying the generalized Syracuse algorithm

G. Leigh (1986)

Acta Arithmetica

A martingale central limit theorem

Petr Lachout (1986)

Commentationes Mathematicae Universitatis Carolinae

A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.

Sethuraman, S., Varadhan, S.R.S. (2005)

Electronic Journal of Probability [electronic only]

A mixed quantum-classical central limit theorem

U. Franz (1998)

Banach Center Publications

A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.

A new semigroup technique in Poisson approximation.

M.L. Puri, D. Pfeifer, P. Deheuvels (1989)

Semigroup forum

A non-commutative central limit theorem.

Roland Speicher (1992)

Mathematische Zeitschrift

A noncommutative limit theorem for homogeneous correlations

Romuald Lenczewski (1998)

Studia Mathematica

We state and prove a noncommutative limit theorem for correlations which are homogeneous with respect to order-preserving injections. The most interesting examples of central limit theorems in quantum probability (for commuting, anticommuting, and free independence and also various q-qclt's), as well as the limit theorems for the Poisson law and the free Poisson law are special cases of the theorem. In particular, the theorem contains the q-central limit theorem for non-identically distributed variables,...

A nonergodic version of Gordin's CLT for integrable stationary processes

Dalibor Volný (1987)

Commentationes Mathematicae Universitatis Carolinae

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