In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius
Author: Maria Eulália Vares
Publisher: Springer Nature
Total Pages: 819
Release: 2021-03-25
Genre: Mathematics
ISBN: 3030607542

This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

In and Out of Equilibrium 2

In and Out of Equilibrium 2
Author: Vladas Sidoravicius
Publisher: Springer Science & Business Media
Total Pages: 570
Release: 2008-11-26
Genre: Mathematics
ISBN: 3764387866

This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom have been personally responsible for advances in the various subfields of probability.

50 Years of First-Passage Percolation

50 Years of First-Passage Percolation
Author: Antonio Auffinger
Publisher: American Mathematical Soc.
Total Pages: 169
Release: 2017-12-20
Genre: Mathematics
ISBN: 1470441837

First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved. In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a learning tool for researchers.

In and Out of Equilibrium

In and Out of Equilibrium
Author: Vladas Sidoravicius
Publisher: Springer Science & Business Media
Total Pages: 484
Release: 2002-04-26
Genre: Mathematics
ISBN: 9780817642891

This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom were personally responsible for advances in the various subfields of probability. Graduate students and researchers in probability theory and math physics will find this book a useful reference.

A First Course in Stochastic Calculus

A First Course in Stochastic Calculus
Author: Louis-Pierre Arguin
Publisher: American Mathematical Society
Total Pages: 270
Release: 2021-11-22
Genre: Mathematics
ISBN: 1470464888

A First Course in Stochastic Calculus is a complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes. This book is also an essential tool for finance professionals who wish to sharpen their knowledge and intuition about stochastic calculus. Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and to random processes governed by the principles of stochastic calculus. The beauty and power of the subject are made accessible to readers with a basic knowledge of probability, linear algebra, and multivariable calculus. This is achieved by emphasizing numerical experiments using elementary Python coding to build intuition and adhering to a rigorous geometric point of view on the space of random variables. This unique approach is used to elucidate the properties of Gaussian processes, martingales, and diffusions. One of the book's highlights is a detailed and self-contained account of stochastic calculus applications to option pricing in finance. Louis-Pierre Arguin's masterly introduction to stochastic calculus seduces the reader with its quietly conversational style; even rigorous proofs seem natural and easy. Full of insights and intuition, reinforced with many examples, numerical projects, and exercises, this book by a prize-winning mathematician and great teacher fully lives up to the author's reputation. I give it my strongest possible recommendation. —Jim Gatheral, Baruch College I happen to be of a different persuasion, about how stochastic processes should be taught to undergraduate and MA students. But I have long been thinking to go against my own grain at some point and try to teach the subject at this level—together with its applications to finance—in one semester. Louis-Pierre Arguin's excellent and artfully designed text will give me the ideal vehicle to do so. —Ioannis Karatzas, Columbia University, New York

Statistical Mechanics of Lattice Systems

Statistical Mechanics of Lattice Systems
Author: Sacha Friedli
Publisher: Cambridge University Press
Total Pages: 643
Release: 2017-11-23
Genre: Mathematics
ISBN: 1107184827

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Noise Sensitivity of Boolean Functions and Percolation

Noise Sensitivity of Boolean Functions and Percolation
Author: Christophe Garban
Publisher: Cambridge University Press
Total Pages: 223
Release: 2015
Genre: Computers
ISBN: 1107076439

This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

Metastability

Metastability
Author: Anton Bovier
Publisher: Springer
Total Pages: 578
Release: 2016-02-11
Genre: Mathematics
ISBN: 3319247778

This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.

Probability on Graphs

Probability on Graphs
Author: Geoffrey Grimmett
Publisher: Cambridge University Press
Total Pages: 279
Release: 2018-01-25
Genre: Mathematics
ISBN: 1108542999

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.