Open AccessBook
Random Walk: A Modern Introduction
Gregory F. Lawler,Vlada Limic +1 more
Reads0
Chats0
TLDR
This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice and is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.Abstract:
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.read more
Citations
More filters
Journal ArticleDOI
Gaussian multiplicative chaos and applications: A review
Rémi Rhodes,Vincent Vargas +1 more
TL;DR: The theory of Gaussian multiplicative chaos was introduced by Kahane's seminal work in 1985 as discussed by the authors, and it has been applied in many applications, ranging from finance to quantum gravity.
MonographDOI
Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction
Sacha Friedli,Yvan Velenik +1 more
TL;DR: In this paper, the authors give a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kac interactions.
Journal ArticleDOI
Lazy Random Walks for Superpixel Segmentation
TL;DR: A novel image superpixel segmentation approach using the proposed lazy random walk (LRW) algorithm with self-loops has the merits of segmenting the weak boundaries and complicated texture regions very well by the new global probability maps and the commute time strategy.
Posted Content
Price dynamics in a Markovian limit order market
Rama Cont,Adrien de Larrard +1 more
TL;DR: In this paper, a simple stochastic model for the dynamics of a limit order book is proposed, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system.
Journal ArticleDOI
Sub-Markov Random Walk for Image Segmentation
TL;DR: The experimental results demonstrate that the proposed subRW method outperforms previous RW algorithms for seeded image segmentation, and designs a new subRW algorithm with label prior to solve the segmentation problem of objects with thin and elongated parts.
References
More filters
Book
Principles of random walk
TL;DR: In this article, a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space, is studied, and the author considered this high degree of specialization worth while because of the theory of such random walks is far more complete than that of any larger class of Markov chains.
Book
Normal Approximation and Asymptotic Expansions
Rabi Bhattacharya,R. Ranga Rao +1 more
TL;DR: In this paper, the Euler-MacLaurin sum formula for functions of several variables has been applied to the problem of convergence of probability measures and uniformity classes, and it has been shown that it is possible to obtain strong convergence for continuous, singular, and discrete probability measures.
Book
Intersections of random walks
TL;DR: In this paper, simple random walks and loop-erased walks are described. But they do not consider intersection probabilities and are not self-avoiding or loop-errasing.
Book ChapterDOI
Conformal invariance of planar loop-erased random walks and uniform spanning trees
TL;DR: In this article, it was shown that the scaling limit of a loop-erased random walk in a simply connected domain is equal to the radial SLE2 path, and that the limit exists and is conformally invariant.