Related papers: Condenser physics applied to Markov chains - A bri…
We give a brief introduction to chiral perturbation theory in its various settings. We discuss some applications of recent interest including chiral extrapolations for lattice gauge theory.
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
We review origins and developments of Noncommutative Potential theory as underpinned by the notion of energy form. Recent and new applications are shown to approximation properties of von Neumann algebras.
The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained…
In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal…
Previous work of Ayyer, Martin, and Williams gave a probabilistic interpretation of the Macdonald polynomials $P_{\lambda}(x_1,\dots,x_n;1,t)$ at $q=1$ in terms of a Markov chain called the multispecies $t$-Push TASEP, a Markov chain…
We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
We discuss a couple of examples of Markov chains. This note is written primarily for school students; it is based on a lecture given by the first author at a Math Circle at NAS (www.assagames.com/nas).
Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $\pi$. Let $\Psi$ a function on the state space of the chain, with $\alpha$-tails with respect to $\pi$, $\alpha\in (0,2)$. We find sufficient conditions on the…
We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the…
In this introductory course we sketch the framework of quantum probability in order to discuss open quantum systems, in particular the damped harmonic oscillator.
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher…
We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop…
These notes are based on lectures given at the XIX Modave School on Mathematical Physics and present an introduction to Exceptional Field Theory. We cover the standard Kaluza-Klein reductions on tori, with applications to supergravity. We…
The electrical conductivity in dense plasmas can be calculated with the relaxation-time approximation provided that the interaction potential between the scattering electron and the ion is known. To date there has been considerable…
In these lectures we give a brief introduction to perturbative and non-perturbative string theory. The outline is the following: 1. Introduction to perturbative string theory 1.1 From point particle to extended objects 1.2 Free closed and…
Thermodynamic stable interaction pair potentials which are not of the form ``positive function + real continuous function of positive type'' are presented in dimension one. Construction of such a potential in dimension two is sketched.…
The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological…