Siti

Random Walks, Markov Chains and the Monte Carlo Method - English
URL: http://www.taygeta.com/rwalks/rwalks.html

A look at some of the practical considerations when making calculations based upon Monte Carlo type methods. The kind of Monte Carlo calculation we will consider. Random number generation. Pseudo-random numbers. Quasi-random numbers. Nonuniform distributions. Monte Carlo integration with quasi-random numbers. Solution to large linear algebra problems using Markov chains. Generalization to solution of integral equations.

[ eng ]

Random Walks and Anomalous Diffusion - English
URL: http://chaos.ph.utexas.edu/research/annulus/rwalk.html

Work done by Eric Weeks, Jeff Urbach, and Harry Swinney. Related to work done by those three and Tom Solomon. This page maintained by Eric Weeks. You may be interested in a paper we wrote for Nonlinear Science Today, which is available over the web.

[ eng ]

Tie Knots and Random Walks - English
URL: http://www.tcm.phy.cam.ac.uk/~ym101/tie4/tie4.html

We introduce a mathematical model of tieknots to classify necktie knots with respect to size and shape. It turns out that tying a tie knots is equivalent to a so-called persistent random walks on a triangular lattice. Using this model, the number of all possible knots in each class (set by the number of total and centre moves respectively) is calculated. The optimal knot in each class is determined by the aesthetic conditions of symmetry and balance. Of the 85 tie knots found, our model duly predicts the four knots in widespread use and further introduces nine new aesthetic ones.

[ eng ]

Reversible Markov Chains and Random Walks on Graphs - English
URL: http://stat-www.berkeley.edu/users/aldous/book.html

by Aldous and Fill: monograph in preparation.

[ eng ]

Random Walk -- from MathWorld - English
URL: http://mathworld.wolfram.com/RandomWalk.html

A random process consisting of a sequence of discrete steps of fixed length. The random thermal perturbations in a liquid are responsible for a random walk phenomenon known as Brownian motion, and the collisions of molecules in a gas are a random walk responsible for diffusion. Random walks have interesting mathematical properties that vary greatly depending on the dimension in which the walk occurs and whether it is confined to a lattice.

[ eng ]