Random walks and hyperplane arrangements
نویسندگان
چکیده
منابع مشابه
Functions of random walks on hyperplane arrangements
Article history: Received 14 December 2009 Accepted 5 February 2010 Available online 24 March 2010 MSC: primary 60J10 secondary 52C35
متن کاملConvex hulls of random walks, hyperplane arrangements, and Weyl chambers
We give an explicit formula for the probability that the convex hull of an n-step random walk in R does not contain the origin, under the assumption that the distribution of increments of the walk is centrally symmetric and puts no mass on affine hyperplanes. This extends the formula by Sparre Andersen (Skand Aktuarietidskr 32:27–36, 1949) for the probability that such random walk in dimension ...
متن کاملRandom Walk and Hyperplane Arrangements
Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...
متن کاملBranched Polymers and Hyperplane Arrangements
We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie [BI], and Kenyon and Winkler [KW] to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the chara...
متن کاملArtin groups and hyperplane arrangements
These are the notes of a mini-course given at the conference “Arrangements in Pyrénées”, held in Pau (France) from 11th to 15th of June, 2012. Definition. Let S be a finite set. A Coxeter matrix on S is a square matrix M = (ms,t)s,t∈S indexed by the elements of S and satisfying: (a) ms,s = 1 for all s ∈ S; (b) ms,t = mt,s ∈ {2, 3, 4, . . . } ∪ {∞} for all s, t ∈ S, s 6= t. A Coxeter matrix is u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1998
ISSN: 0091-1798
DOI: 10.1214/aop/1022855884