We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs wit...Lasīt vairāk
Stochastic analysis tackles randomness in physical systems by blending simulation methods with hands-on problem-solving strategies. It examines key concepts like Markov chains, Gaussian processes, Ito calculus and stochastic differential equations,...Lasīt vairāk
Mathematical ideas unite Statistical Mechanics and Conformal Field Theory by charting a path from two-dimensional lattice models and phase transitions to the emergence of 2D CFT, focusing on Unitary Minimal Models. Scaling assumptions and probabilis...Lasīt vairāk
In this article we provide conditions on the coefficient functions of the stochastic differential equation and on p ? (0, ?) that are sufficient for local Lipschitz continuity in the strong Lp-sense with respect to the initial value and we establish...Lasīt vairāk
It is a longstanding unsolved problem to characterize the optimal feedbacks for general SLQs with random coefficients in infinite dimensions; the same problem but in finite dimensions was addressed very recently. This paper is devoted to giving a so...Lasīt vairāk
The objective of the present study is to develop an approach for a large class of deterministic scatterer configurations, including various types of quasicrystals. We prove the convergence of the particle dynamics to transport processes that are in...Lasīt vairāk
Samopriya Basu, Troy Butler, Don Estep, Nishant Panda
Sērija : Computational Science and Engineering
(Izdošanas datums: 31-Mar-2024, Paperback / softback, Izdevniecība: Society for Industrial & Applied Mathematics,U.S., ISBN-13: 9781611977813)
Brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing comm...Lasīt vairāk
We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host Kra seminorms. Our main result yields a complete structural description of cubic couplings, using...Lasīt vairāk
Provides a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is in...Lasīt vairāk
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a mod...Lasīt vairāk
This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of...Lasīt vairāk
Based on lectures the author gave as part of the U. of Chicago Research Experiences for Undergraduates program in 2020, this book discusses aspects of objects that arise in models in probability and statistical mechanics, focusing on discrete mod...Lasīt vairāk
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest c...Lasīt vairāk
Harmonic analysis is the study of functions by decomposing them into components that are special functions, says Varadhan, and he considers here only those aspects of the vast field that were part of the course he taught at the Courant Institute...Lasīt vairāk
This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of...Lasīt vairāk
