Title: A characterization of a class of random variables in terms of the number operator
Speaker: Aurel Stan (The Ohio State University)
Speaker's URL: https://math.osu.edu/people/stan.7
Abstract: If a random variable, $X$, has finite moments of all orders, then its moments can be recovered from its number operator $N$. In this talk we study the random variables $X$, for which there exist two polynomials, $P$ and $Q$, of degree at most 2, such that:
\[
[[P(N), X], X] = Q(X),
\]
where $[A$, $B]$ denotes the commutator of the operators $A$ and $B$. These random variables include the Gaussian, Gamma, and beta distributions, which correspond to the Hermite, Laguerre, and Jacobi orthogonal polynomials.
URL associated with Seminar: https://u.osu.edu/aots/
