Brownian Motion, Obstacles and Random Media

Author: Alain-Sol Sznitman

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 357

View: 529

This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.

Dynamics and Randomness II

Author: Alejandro Maass

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 228

View: 752

This book contains the lectures given at the Second Conference on Dynamics and Randomness held at the Centro de Modelamiento Matemático of the Universidad de Chile, from December 9-13, 2003. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. The courses were on: -Some Aspects of Random Fragmentations in Continuous Times; -Metastability of Ageing in Stochastic Dynamics; -Algebraic Systems of Generating Functions and Return Probabilities for Random Walks; -Recurrent Measures and Measure Rigidity; -Stochastic Particle Approximations for Two-Dimensional Navier Stokes Equations; and -Random and Universal Metric Spaces. The intended audience for this book is Ph.D. students on Probability and Ergodic Theory as well as researchers in these areas. The particular interest of this book is the broad areas of problems that it covers. We have chosen six main topics and asked six experts to give an introductory course on the subject touching the latest advances on each problem.

Applied Stochastic Analysis

Author: Weinan E

Publisher: American Mathematical Soc.


Category: Stochastic analysis

Page: 305

View: 243

This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.

Directed Polymers in Random Environments

École d'Été de Probabilités de Saint-Flour XLVI – 2016

Author: Francis Comets

Publisher: Springer


Category: Mathematics

Page: 199

View: 233

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

Stochastic Analysis on Large Scale Interacting Systems

Author: Tadahisa Funaki

Publisher: Mathematical Soc of Japan


Category: Mathematics

Page: 395

View: 895

This volume is a collection of 15 research and survey papers written by the speakers from two international conferences held in Japan, The 11th Mathematical Society of Japan International Research Institute's Stochastic Analysis on Large Scale Interacting Systems and Stochastic Analysis and Statistical Mechanics. Topics discussed in the volume cover the hydrodynamic limit, fluctuations, large deviations, spectral gap (Poincare inequality), logarithmic Sobolev inequality, Ornstein-Zernike asymptotics, random environments, determinantal expressions for systems including exclusion processes (stochastic lattice gas, Kawasaki dynamics), zero range processes, interacting Brownian particles, random walks, self-avoiding walks, Ginzburg-Landau model, interface models, Ising model, Widom-Rowlinson model, directed polymers, random matrices, Dyson's model, and more. The material is suitable for graduate students and researchers interested in probability theory, stochastic processes, and statistical mechanics.