Local behavior and hitting probabilities of the Airy process
Author
dc.contributor.author
Quastel, Jeremy
Author
dc.contributor.author
Remenik Zisis, Daniel
es_CL
Admission date
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2014-01-09T15:23:40Z
Available date
dc.date.available
2014-01-09T15:23:40Z
Publication date
dc.date.issued
2013
Cita de ítem
dc.identifier.citation
Probab. Theory Relat. Fields (2013) 157:605–634
en_US
Identifier
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DOI 10.1007/s00440-012-0466-8
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/126118
General note
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Artículo de publicación ISI
en_US
Abstract
dc.description.abstract
We obtain a formula for the n-dimensional distributions of the Airy
process in terms of a Fredholm determinant on L2(R), as opposed to the standard
formula which involves extended kernels, on L2({1, . . . , n} × R). The formula is
analogous to an earlier formula of Prähofer and Spohn (J Stat Phys 108(5–6):1071–
1106, 2002) for the Airy2 process. Using this formula we are able to prove that the
Airy process is Hölder continuous with exponent 1
2—and that it fluctuates locally
like a Brownian motion.We also explain how the same methods can be used to obtain
the analogous results for the Airy process. As a consequence of these two results, we
derive a formula for the continuum statistics of the Airy1 process, analogous to that
obtained in Corwin et al. (CommunMath Phys 2012, to appear) for the Airy process.