Gaussian fluctuations for the directed polymer partition function in dimension d≥3 and in the whole L2-region
| Autor: | Shuta Nakajima, Clément Cosco |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Partition function (quantum field theory) Gaussian Mathematical analysis Martingale central limit theorem Normal distribution symbols.namesake Distribution (mathematics) Rate of convergence symbols Limit (mathematics) Statistics Probability and Uncertainty Scaling Mathematics |
| Zdroj: | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 57 |
| ISSN: | 0246-0203 |
| DOI: | 10.1214/20-aihp1100 |
| Popis: | We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail n(d−2)/4(W∞−Wn) of the normalized partition function. It was proven by Comets and Liu (J. Math. Anal. Appl. 455 (2017) 312–335), that for sufficiently high temperature, the fluctuations converge in distribution towards the product of the limiting partition function and an independent Gaussian random variable. We extend the result to the whole L2-region of temperature, which is predicted to be the maximal high-temperature region where the Gaussian fluctuations should occur under the considered scaling. To do so, we manage to avoid the heavy 4th-moment computation and instead rely on the local limit theorem for polymers (Fund. Math. 147 (1995) 173–180; Ann. Inst. Henri Poincare Probab. Stat. 42 (2006) 521–534) and homogenization. |
| Databáze: | OpenAIRE |
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