Random Walks on Trees and Matchings
نویسندگان
چکیده
منابع مشابه
Random Walks on Trees and Matchings
We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vertices. Roughly, the results show that 1 2 n log n steps are necessary and suffice to achieve randomness. The proof depends on the representation theory of the symmetric group and a bijection between...
متن کاملOptimal Random Matchings on Trees and Applications
In this paper we will consider tight upper and lower bounds on the weight of the optimal matching for random point sets distributed among the leaves of a tree, as a function of its cardinality. Specifically, given two n sets of points R = {r1, ..., rn} and B = {b1, ..., bn} distributed uniformly and randomly on the m leaves of λ-Hierarchically Separated Trees with branching factor b such that e...
متن کاملRandom walks on complex trees.
We study the properties of random walks on complex trees. We observe that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case. Second, the mean first passage time (MFPT) display...
متن کاملRandom Walks on Rooted Trees
For arbitrary positive integers h and m, we consider the family of all rooted trees of height h having exactly m vertices at distance h from the root. We refer to such trees as (h,m)-trees. For a tree T from this family, we consider a simple random walk on T which starts at the root and terminates when it visits one of the m vertices at distance h from the root. Consider the problem of finding ...
متن کاملRandom Walks and Trees
These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to ...
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: Electronic Journal of Probability
سال: 2002
ISSN: 1083-6489
DOI: 10.1214/ejp.v7-105