Related papers: Infinitesimal generators for a class of polynomial…

A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…

We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in our previous papers and can be regarded as a random joint of two…

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…

We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.

The dynamics of a Markov process are often specified by its infinitesimal generator or, equivalently, its symbol. This paper contains examples of analytic symbols which do not determine the law of the corresponding Markov process uniquely.…

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.

It is known that many constructions arising in the classical Gaussian infinite dimensional analysis can be extended to the case of more general measures. One such extension can be obtained through biorthogonal systems of Appell polynomials…

The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…

We describe several families of permutation polynomials obtained using functions with linear translators.

We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.

Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…

We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature using the connections of these objects to Young tableaux and…

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…

We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a…

We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed formula for its order.

We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…

For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant…

Given two polynomials $p(x), q(x)$ of degree $d$, we give a combinatorial formula for the finite free cumulants of $p(x)\boxtimes_d q(x)$. We show that this formula admits a topological expansion in terms of non-crossing multi-annular…