Related papers: Grassmannian calculus for probability
These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by…
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of…
This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…
This paper is based on a talk presented by the first author at the Short Program on Riemannian Geometry that took place at the Centre de Recherche Math\'ematiques, Universit\'e de Montr\'eal, during the period June 28-July 16, 2004. It is a…
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
Coulomb gases are special probability distributions, related to potential theory, that appear at many places in pure and applied mathematics and physics. In these short expository notes, we focus on some models, ideas, and structures. We…
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed…
The following technical report presents a formal approach to probabilistic minimalist grammar parameter estimation. We describe a formalization of a minimalist grammar. We then present an algorithm for the application of variational…
This paper is based on four lectures given at the Trieste Summer School 1994 on theories of fermion masses. The first two lectures introduce three mechanisms which have been used to construct models of fermion masses. We then discuss some…
These lecture notes collect the material that I have been using over the years for various short courses on the physics of gravitational waves, first at the Institut d'Astrophysique de Paris (France), and then at SISSA (Italy) and various…