Central Limit Theorem for the Edwards Model
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 lar...
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| Veröffentlicht in: | The Annals of probability 1997-04, Vol.25 (2), p.573-597 |
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| container_end_page | 597 |
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| container_issue | 2 |
| container_start_page | 573 |
| container_title | The Annals of probability |
| container_volume | 25 |
| creator | van der Hofstad, R. den Hollander, F. Konig, W. |
| description | 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). |
| doi_str_mv | 10.1214/aop/1024404412 |
| format | Article |
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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. 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| ispartof | The Annals of probability, 1997-04, Vol.25 (2), p.573-597 |
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| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aop_1024404412 |
| source | Jstor Complete Legacy; JSTOR Mathematics and Statistics; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete |
| subjects | 60F05 60J55 60J65 Bleeding time Brownian motion Central limit theorem Edwards model Eigenfunctions Eigenvalues Exact sciences and technology Infinity Limit theorems Markov processes Martingales Mathematical analysis Mathematics Operator theory Polymers Probability and statistics Probability theory and stochastic processes Ray-Knight theorems Sciences and techniques of general use Transition probabilities |
| title | Central Limit Theorem for the Edwards Model |
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