publication . Preprint . 2020

The random walk penalised by its range in dimensions $d\geq 3$

Berestycki, Nathanael; Cerf, Raphaël;
Open Access English
  • Published: 03 Mar 2020
  • Country: France
Comment: Revised version, local errors and typos corrected
arXiv: Mathematics::Probability
free text keywords: Mathematics - Probability, [MATH]Mathematics [math], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]

[4] Marek Biskup and Eviatar B Procaccia. Shapes of drums with lowest base frequency under non-isotropic perimeter constraints. arXiv preprint arXiv:1603.03871, 2016.

[6] Erwin Bolthausen. Localization of a two-dimensional random walk with an attractive path interaction. Ann. Probab., 22(2):875{918, 1994. [OpenAIRE]

[7] Lorenzo Brasco, Guido De Philippis, and Bozhidar Velichkov. Faber-Krahn inequalities in sharp quantitative form. Duke Math. J., 164(9):1777{1831, 2015.

[9] M. D. Donsker and S. R. S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. I. II. Comm. Pure Appl. Math., 28:1{47; ibid. 28 (1975), 279{301, 1975. [OpenAIRE]

[10] M. D. Donsker and S. R. S. Varadhan. On the number of distinct sites visited by a random walk. Comm. Pure Appl. Math., 32(6):721{747, 1979. [OpenAIRE]

[11] Richard S. Ellis. Entropy, large deviations, and statistical mechanics. Classics in Mathematics. Springer-Verlag, Berlin, 2006. Reprint of the 1985 original.

[12] K. Fan. Minimax theorems. Proc. Nat. Acad. Sci., 39:42{47, 1953.

[13] Nicola Fusco, Francesco Maggi, and Aldo Pratelli. Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 8(1):51{71, 2009.

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