Directed polymers in random environments
著者
書誌事項
Directed polymers in random environments
（Lecture notes in mathematics, 2175 . École d'été de probabilités de Saint-Flour ; 46-2016）
Springer, c2017
大学図書館所蔵 件 / 全38件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 187-196) and index
内容説明・目次
内容説明
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.
目次
1 Introduction.- 2 Thermodynamics and Phase Transition.- 3 The martingale approach and the L2 region.- 4 Lattice versus tree.- 5 Semimartingale approach and localization transition.- 6 Log-Gamma polymer model.- 7 Kardar-Parisi-Zhang equation and universality.- 8 Variational formulas.
「Nielsen BookData」 より