Loop-erased Random Walk Research Articles

Loop-erased self-avoiding random walk in two and three dimensions

IfŜ(n) is the position of the self-avoiding random walk in ℤ d obtained by erasing loops from simple random walk, then it is proved that the mean square displacementE(¦Ŝ(n)¦2) grows at least as fast as the Flory predictions for the usual SAW, i.e., at least as fast asn3/2 ford=2 andn6/5 ford=3. In particular, if the mean square displacement of the usual SAW grows liken1.18... ind=3, as expected, then the loop-erased process is in a different universality class.

Loop-erased self-avoiding random walk and the Laplacian random walk

Comments that the Laplacian random walk with eta =1, recently introduced by Lyklema and Evertsz (1986), is the same process as the loop-erased self-avoiding random walk analysed previously by the author (1980). Some rigorous results about this process are reviewed.

Gaussian behavior of loop-erased self-avoiding random walk in four dimensions

Une marche auto-evitante de longueur n sur le reseau entier Z d est une suite ordonnee de points [x 0 =0, x 1 ,...,x n ] avec |x i −x i−1 |=1 et x i ¬=x j pour i¬=j. On etudie le comportement d'une telle marche a d=4 quand on applique le processus de boucle effacee

A connective constant for loop-erased self-avoiding random walk

A ‘connective constant' is defined for self-avoiding random walk derived by erasing loops from simple random walk. For d ≧ 5, it is shown that this distribution on n-step self-avoiding paths approaches a uniform distribution in a weak sense.

A connective constant for loop-erased self-avoiding random walk

A ‘connective constant' is defined for self-avoiding random walk derived by erasing loops from simple random walk. For d ≧ 5, it is shown that this distribution on n-step self-avoiding paths approaches a uniform distribution in a weak sense.

On the Rate of Convergence for the Invariance Principle

On the Rate of Convergence for the Invariance Principle