Related papers: Lectures on integrable probability
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
Dynamical two-particle susceptibilites are important for a wide range of different experiments in condensed-matter physics and beyond. Nevertheless, most textbooks avoid describing how to derive such response functions, perhaps because they…
The use of coordinate processes for the modelling of impulse control for general Markov processes typically involves the construction of a probability measure on a countable product of copies of the path space. In addition, admissibility of…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
Markov decision processes (MDPs) are formal models commonly used in sequential decision-making. MDPs capture the stochasticity that may arise, for instance, from imprecise actuators via probabilities in the transition function. However, in…
These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.
Machine learning is used to generate empirical pseudopotentials that characterize the local screened interactions in the Kohn-Sham Hamiltonian. Our approach incorporates momentum-range-separated rotation-covariant descriptors to capture…
This paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on micro-macro (or multiscale) models. Some elements of mathematical and numerical analysis are provided. These notes closely follow the lectures…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
Original paper: We revisit the probability that any two consecutive events in a Poisson process N on [0,t] are separated by a time interval which is greater than s(<t) (a particular scan statistic probability), and the closely related…
Lecture notes for a master-level applied mathematics course on stochastic processes and applications, held at the University of Orl\'eans, France. Contents: Markov chains, Poisson point processes, Markovian jump processes, queueing theory.…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till…
This article provides an introductory tutorial on structural results in partially observed Markov decision processes (POMDPs). Typically, computing the optimal policy of a POMDP is computationally intractable. We use lattice program- ming…
This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…
Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…
I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the…