Directed Polymers in Random Environments - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Directed Polymers in Random Environments write by Francis Comets. This book was released on 2017-01-26. Directed Polymers in Random Environments available in PDF, EPUB and Kindle. 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.
The Directed Polymer in a Random Environment
The Directed Polymer in a Random Environment - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Directed Polymer in a Random Environment write by John M. Noble. This book was released on 1996. The Directed Polymer in a Random Environment available in PDF, EPUB and Kindle.
Random Polymers
Random Polymers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Polymers write by Frank den Hollander. This book was released on 2009-04-09. Random Polymers available in PDF, EPUB and Kindle. Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.
A Condition for Weak Disorder for Directed Polymers in Random Environment
A Condition for Weak Disorder for Directed Polymers in Random Environment - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Condition for Weak Disorder for Directed Polymers in Random Environment write by Matthias Birkner. This book was released on 2003. A Condition for Weak Disorder for Directed Polymers in Random Environment available in PDF, EPUB and Kindle.
Directed Polymers in Random Media
Directed Polymers in Random Media - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Directed Polymers in Random Media write by Vu-Lan Nguyen. This book was released on 2016. Directed Polymers in Random Media available in PDF, EPUB and Kindle. The thesis focuses on (mostly 1 + 1 dimensional) directed polymers in random media. These are classical and celebrated models in the statistical mechanics of disordered systems and describe a one dimensional interface interacting with a d + 1-dimensional random environment where it is immersed. A very important question is to understand, in the limit where the polymer's length tends to infinity and for a typical realization of the environment, the geometric properties of the polymer: typical transversal displacement of the endpoint and its fluctuations, polymer localization at strong disorder around typical tubes determined by disorder... A strictly related problem of great interest is to study the fluctuations of the free energy. The main focus is on the so-called log-gamma polymer. This model, introduced by Seppalainen, is obtained by making a specific choice for the disorder law: the random variables are inverse Gamma variables. For this specific disorder choice, he proved that the variance of the log of the partition function is of order N"2/3, as expected by KPZ theory. This was refined into a full limit theorem Tracy -Widom type fluctuations) by Corwin, O'Connell, Seppalainen and Zygouras, via an explicit formula for the Laplace transform of a single partition function. It was until now an open problem to compute correlations between partition functions with different end-points and to study the asymptotic distribution of the polymer's endpoint. The present thesis addresses, among others, these two very challenging problems. On the other hand, we consider applications of stochastic orders on the study of directed polymer and disordered systems.
