Disorder, entropy and harmonic functions
| Autor: | Itai Benjamini, Gady Kozma, Hugo Duminil-Copin, Ariel Yadin |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
37A35
Statistics and Probability Pure mathematics Harmonic functions Sublinear function Kaimanovich–Vershik 82B43 planar map random walk in random environment percolation stationary graphs anomalous diffusion FOS: Mathematics Entropy (information theory) Almost surely Uniqueness ddc:510 IIC Heat kernel Mathematics Random graph Avez Probability (math.PR) UIPQ 31A05 20P05 60K37 Harmonic function 60J10 Statistics Probability and Uncertainty entropy corrector 60B15 Mathematics - Probability Vector space |
| Zdroj: | Ann. Probab. 43, no. 5 (2015), 2332-2373 |
| ISSN: | 0091-1798 2332-2373 |
| DOI: | 10.1214/14-aop934 |
| Popis: | We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on $\mathbb{Z}^d$. We prove that the vector space of harmonic functions growing at most linearly is $(d+1)$-dimensional almost surely. Further, there are no nonconstant sublinear harmonic functions (thus implying the uniqueness of the corrector). A main ingredient of the proof is a quantitative, annealed version of the Avez entropy argument. This also provides bounds on the derivative of the heat kernel, simplifying and generalizing existing results. The argument applies to many different environments; even reversibility is not necessary. Published at http://dx.doi.org/10.1214/14-AOP934 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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