Asymptotics for the heat kernel in multicone domains

Pierre Collet, Mauricio Duarte, Servet Martínez, Arturo Prat-Waldron, Jaime San Martín

Resultado de la investigación: Article

Resumen

A multicone domain Ω⊆Rn is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of the heat kernel p(t, x, y) of a Brownian motion killed upon exiting Ω, using both probabilistic and analytical techniques. We find that the decay is polynomial and we characterize p(t, x, y) in terms of the Martin boundary of Ω at infinity, where α>0 depends on the geometry of Ω. We next derive an analogous result for tκ/2Px(T>t), with κ=1+α-n/2, where T is the exit time from Ω. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.

Idioma originalEnglish
Páginas (desde-hasta)1269-1298
Número de páginas30
PublicaciónJournal of Functional Analysis
Volumen270
N.º4
DOI
EstadoPublished - 15 feb 2016

Huella dactilar

Heat Kernel
Decay
Martin Boundary
Exit Time
Connected Set
Brownian motion
Deduce
Cone
Infinity
Polynomial

ASJC Scopus subject areas

  • Analysis

Citar esto

Collet, P., Duarte, M., Martínez, S., Prat-Waldron, A., & San Martín, J. (2016). Asymptotics for the heat kernel in multicone domains. Journal of Functional Analysis, 270(4), 1269-1298. https://doi.org/10.1016/j.jfa.2015.10.021
Collet, Pierre ; Duarte, Mauricio ; Martínez, Servet ; Prat-Waldron, Arturo ; San Martín, Jaime. / Asymptotics for the heat kernel in multicone domains. En: Journal of Functional Analysis. 2016 ; Vol. 270, N.º 4. pp. 1269-1298.
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Collet, P, Duarte, M, Martínez, S, Prat-Waldron, A & San Martín, J 2016, 'Asymptotics for the heat kernel in multicone domains', Journal of Functional Analysis, vol. 270, n.º 4, pp. 1269-1298. https://doi.org/10.1016/j.jfa.2015.10.021

Asymptotics for the heat kernel in multicone domains. / Collet, Pierre; Duarte, Mauricio; Martínez, Servet; Prat-Waldron, Arturo; San Martín, Jaime.

En: Journal of Functional Analysis, Vol. 270, N.º 4, 15.02.2016, p. 1269-1298.

Resultado de la investigación: Article

TY - JOUR

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AU - Duarte, Mauricio

AU - Martínez, Servet

AU - Prat-Waldron, Arturo

AU - San Martín, Jaime

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