Local behavior and hitting probabilities of the Airy process
Artículo

Open/ Download
Publication date
2013Metadata
Show full item record
Cómo citar
Quastel, Jeremy
Cómo citar
Local behavior and hitting probabilities of the Airy process
Author
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.
General note
Artículo de publicación ISI
Quote Item
Probab. Theory Relat. Fields (2013) 157:605–634
Collections