Related papers: A Conversation with Murray Rosenblatt
The numerical phenomenon of $\pi$ appearing at parameters $c = 1/4$, $c=-3/4$ and $c=-5/4$ in the Mandelbrot set $\mathcal{M}$ has been known for over 30 years. In 2001, the first proof was provided by Aaron Klebanoff for the parameter…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.
Despite a previous description of his state as a stable fixed point, just past midnight this morning Mr. Boddy was murdered again. In fact, over 70 years Mr. Boddy has been reported murdered $10^6$ times, while there exist no documented…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
This is an elementary review, aimed at non-specialists, of results that have been obtained for the limiting distribution of eigenvalues and for the operator norms of real symmetric random matrices via the method of moments. This method goes…
This is the first part of an oral history interview on the lifelong involvement of Joel Lebowitz in the development of statistical mechanics. Here the covered topics include the formative years, which overlapped the tragic period of Nazi…
The papers gathered in this collection were presented at the 8th International Workshop on Nonmonotonic Reasoning, NMR2000. The series was started by John McCarthy in 1978. The first international NMR workshop was held at Mohonk Mountain…
In this very personal workography, I relate my 40-year experiences as a researcher and educator in and around Artificial Intelligence (AI), more specifically Natural Language Processing. I describe how curiosity, and the circumstances of…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
Many diseases and traits involve a complex interplay between genes and environment, generating significant interest in studying gene-environment interaction through observational data. However, for lifestyle and environmental risk factors,…
Mike West is currently the Arts & Sciences Distinguished Professor Emeritus of Statistics and Decision Sciences at Duke University. Mike's research in Bayesian analysis spans multiple interlinked areas: theory and methods of dynamic models…
A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
Mendelian randomization (MR) is an epidemiological method that can be used to strengthen causal inference regarding the relationship between a modifiable environmental exposure and a medically relevant trait and to estimate the magnitude of…
A key point in Douady and Hubbard's study of the Mandelbrot set $M$ is the theorem that every parabolic point $c\ne 1/4$ in $M$ is the landing point for exactly two external rays with angle which are periodic under doubling. This note will…
The current status of Doubly Special Relativity research program is shortly presented. I dedicate this paper to my teacher and friend Professor Jerzy Lukierski on occasion of his seventieth birthday.
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…