Related papers: Donald Burkholder's work in martingales and analys…
We give operational formulae of Burchnall type involving complex Hermite polynomials. Short proofs of some known formulae are given and new results involving these polynomials, including Nielsen's identities and Runge addition formula, are…
We derive inequalities for time-discrete and time-continuous martingales that are similar to the well-known Burkholder inequalities. For the time-discrete case arbitrary martingales in $L^p(\Omega)$ are treated, whereas in the…
This is an old talk about Boardman's work in Z/2-equivariant unoriented cobordism. It appeared long ago, but it discusses a useful geometric interpretation of Tate cohomology which doesn't seem to be widely known. I'm posting it in an…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
In this paper we present the definitions and some properties of several Samrandache Type Functions that are involved in many solved and unsolved problems and conjectures in number theory and recreational mathematics.
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
This is a survey on Drinfeld associators and their generalizations, where we focus on operadic aspects.
We prove Davis decompositions for vector valued Hardy martingales and illustrate their use. This paper continues our previous work on Davis and Garsia inequalities for scalar Hardy martingales.
An introduction to Hyperbolic Analysis is presented.
Principles for the planning and analysis of observational studies, as suggested by W.G Cochran in 1972, are discussed and compared to additional methodological developments since then.
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
It has been recently shown that the Bellman function method can be applied in the general context of Gundy's extrapolation theorem for vector-valued martingales. But the additional assumption has been made that martingales are adapted to a…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and…
An expository introduction to bidding chess and other bidding games. To appear in Mathematical Intelligencer.
This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra. We include results from the recent literature building on Stanley's work,…
This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.
Invited contribution to Annalen der Physik (Expert Opinion).
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to obtain several counterparts to well…