Persistence Probability of Random Weyl Polynomial

Probability Bounds for Polynomial Functions in Random Variables

Random sampling is a simple but powerful method in statistics and the design of randomized algorithms. In a typical application, random sampling can be applied to estimate an extreme value, say maximum, of a function f over a set S ⊆ R. To do so, one may select a simpler (even finite) subset S0 ⊆ S, randomly take some samples over S0 for a number of times, and pick the best sample. The hope is ...

The Probability That a Random Monic p-adic Polynomial Splits

Properties of Polynomial Identity Quantized Weyl Algebras

In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. F...

Polynomial Extensions of the Weyl C*-Algebra

We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue of the Weyl C*-algebra and use this result to deduce the explicit form of the composition law of the associated generalization of the 1-dimensional Heisenberg...

Generalized Weyl algebras and diskew polynomial rings

The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called generalized Weyl algebras) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ GWAs. A new class of rings, the diskew polynomial rings, is introduced that is closely related to GWAs (they are GWAs under a mild condition). The, so-called, amb...