The Edwards model in one dimension is a transformed path measure for
standard Brownian motion discouraging self-intersections. We prove a central
limit theorem for the endpoint of the path, extending a law of large numbers
proved by Westwater. The scaled variance is characterized in terms of the
largest eigenvalue of a one-parameter family of differential operators,
introduced and analyzed by van der Hofstad and den Hollander. Interestingly,
the scaled variance turns out to be independent of the strength of
self-repellence and to be strictly smaller than one (the value for free
Brownian motion).
Publié le : 1997-04-14
Classification:
Edwards model,
Ray-Knight theorems,
central limit theorem,
60F05,
60J55,
60J65
@article{1024404412,
author = {van der Hofstad, R. and den Hollander, F. and K\"onig, W.},
title = {Central limit theorem for the Edwards model},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 573-597},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404412}
}
van der Hofstad, R.; den Hollander, F.; König, W. Central limit theorem for the Edwards model. Ann. Probab., Tome 25 (1997) no. 4, pp. 573-597. http://gdmltest.u-ga.fr/item/1024404412/