Central limit theorem for the Edwards model
- 1 April 1997
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 25 (2) , 573-597
- https://doi.org/10.1214/aop/1024404412
Abstract
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).Keywords
This publication has 9 references indexed in Scilit:
- A central limit theorem for a one-dimensional polymer measureThe Annals of Probability, 1996
- Scaling for a random polymerCommunications in Mathematical Physics, 1995
- Markovian Bridges: Construction, Palm Interpretation, and SplicingPublished by Springer Nature ,1993
- Continuous Martingales and Brownian MotionPublished by Springer Nature ,1991
- Sur la loi des temps locaux browniens pris en un temps exponentielPublished by Springer Nature ,1988
- Un processus qui ressemble au pont BrownienPublished by Springer Nature ,1987
- Markov ProcessesPublished by Wiley ,1986
- Application de la theorie du grossissement a l'etude des temps locaux BrowniensPublished by Springer Nature ,1985
- Local time is a semi-martingaleProbability Theory and Related Fields, 1982