Donsker, M. D.; Varadhan, S. R. S. Asymptotics for the polaron. (English) Zbl 0538.60081 Commun. Pure Appl. Math. 36, 505-528 (1983). The polaron problem, the calculation of the asymptotic behaviour of an expectation value with respect to three dimensional Brownian motion tied down at both ends, is solved. Also the conjecture of S. I. Pekar [Theory of polarons. Zh. Ekhsperim. Teor. Fiz. 19 (1949)] is proved. The authors use large deviation results given in earlier papers on the asymptotic evaluation of certain Markov process expectations for large time. Reviewer: G.Gerlich Cited in 7 ReviewsCited in 76 Documents MSC: 60J65 Brownian motion 60F10 Large deviations 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:polaron problem; three dimensional Brownian motion tied down at both ends; expectations for large time × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Statistical Mechanics, W. A. Benjamin, Reading, MA, 1972. [2] Pekar, Zh. Eksperim. i Teor. Fiz. 19 (1949) [3] Donsker, Comm. Pure Appl. Math. 28 pp 1– (1975) [4] Comm. Pure Appl. Math. 28 pp 279– (1975) [5] Comm. Pure Appl. Math. 29 pp 389– (1976) [6] Donsker, IV, Comm. Pure Appl. Math. 36 pp 183– (1983) [7] , and , Strong coupling limit of polaron energy, revisited, Physical Letter, Sept. 1980, pp. 249–251. [8] Lieb, Studies in Applied Mathematics 57 pp 93– (1977) · Zbl 0369.35022 · doi:10.1002/sapm197757293 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.