Нелинейная динамика
  • формат pdf
  • размер 1.38 МБ
  • добавлен 07 мая 2011 г.
Garban C., Steif J. Lectures on Noise Sensitivity and Percolation
Publisher: arXiv, 2011. - 150 pages.

The goal of this set of lectures is to combine two seemingly unrelated topics:

- The study of Boolean functions, a field particularly active in computer science;
- Some models in statistical physics, mostly percolation.

The link between these two fields can be loosely explained as follows: a percolation configuration is built out of a collection of i.i.d "bits" which determines whether the corresponding edges, sites, or blocks are present or absent. In that respect, any event conceing percolation can be seen as a Boolean function whose input are precisely these "bits".

Over the last 20 years, mainly thanks to the computer science community, a very rich structure has emerged conceing the properties of Boolean functions. The first part of this course will be devoted to a description of some of the main achievements in this field. In some sense one can say, although this is an exaggeration, that computer scientists are mostly interested in the stability or robustness of Boolean functions. As we will see later in this course, the Boolean functions which "encode" large scale properties of critical percolation will tu out to be very sensitive to small perturbations. This phenomenon corresponds to what we will call noise sensitivity. Hence, the Boolean functions one wishes to describe here are in some sense orthogonal to the Boolean
functions one encounters, ideally, in computer science. Remarkably, it tus out that the tools developed by the computer science community to capture the properties and stability of Boolean functions are also suitable for the study of noise sensitive functions. This is why it is worth us first spending some time on the general properties of Boolean functions.
Похожие разделы
Смотрите также

Carr J. Applications Of Centre Manifold Theory

  • формат djvu
  • размер 671.27 КБ
  • добавлен 26 января 2011 г.
Springer, 1981. - 142 pages. These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope th...

Evans L.C. An Introduction to Stochastic Differential Equations

  • формат pdf
  • размер 1.28 МБ
  • добавлен 26 января 2011 г.
UC Berkeley, 2006. - 139 pages. These notes survey, without too many precise details, the basic theory of probability, random differential equations and some applications. A really careful treatment assumes the students' familiarity with probability theory, measure theory, ordinary differential equations, and partial differential equations as well. The author tried to design these lectures so that starting graduate students can follow most of th...

Horsthemke W., Lefever R. Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology

  • формат pdf
  • размер 15.63 МБ
  • добавлен 06 ноября 2011 г.
Springer-Verlag Berlin, 2006, 318 pages This classic text, an often-requested reprint, develops and explains the foundations of noise-induced processes. At its core is a self-contained, textbook-style presentation of the elements of probability theory, of the theory of Markovian diffusion processes and of the theory of stochastic differential equations, on which the modeling of fluctuating natural and artificial environments is based. Following...

Korsch H.J., Jodl H.-J. Chaos: a program collection for the PC; with many numerical experiments

  • формат pdf
  • размер 14.34 МБ
  • добавлен 27 февраля 2011 г.
Springer-verlag, 2008. 352 р. ISBN 978-3-540-63893-3 (2nd ed. ) This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant...

Lai Y.-C., Tel T. Transient Chaos: Complex Dynamics on Finite Time Scales

  • формат pdf
  • размер 8.93 МБ
  • добавлен 11 апреля 2011 г.
Springer, 2011. - 538 pages. In a dynamical system, transients are temporal evolutions preceding the asymptotic dynamics. Transient dynamics can be more relevant than the asymptotic states of the system in terms of the observation, modeling, prediction, and control of the system. As a result, transients are important to dynamical systems arising from a wide range of disciplines such as physics, chemistry, biology, engineering, economics, and eve...

Lee K.K. Lectures on Dynamical Systems, Structural Stability and Their Applications

  • формат pdf
  • размер 26.56 МБ
  • добавлен 21 ноября 2011 г.
World Scientific Publishing, 1992, 454 pages. This book is based on a graduate course for scientists and engineers. The author's style is clear, formulations of mathematical results are precise. The book helps the reader to create a good global picture of the theory of dynamical systems. The author has gathered a considerable number of facts about dynamical systems in this book, including almost 1000 references, so that it can also serve as a ha...

Zehnder E. Lectures on Dynamical Systems: Hamiltonian Vector Fields and Symplectic Capacities

  • формат pdf
  • размер 4.2 МБ
  • добавлен 11 апреля 2011 г.
European Mathematical Society, 2010. - 363 pages. This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearb...