Local behavior and hitting probabilities of the \(\text{Airy}_1\) process
type: Item
instance of: scholarly article
title: Local behavior and hitting probabilities of the \(\text{Airy}_1\) process
zbMATH Open document ID: 1285.60095
author: J. D. Quastel
author: Daniel Remenik
publication date: 2014-01-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.4709
review text: The authors produce a formula for the \(n\)-dimensional distributions of the \(\text{Airy}_1\) process in terms of a Fredholm determinant on \(L^2(\mathbb{R}),\) as opposed to the standard formula which involves extended kernels, on \(L^2(\{1,\dots,n\} \times\mathbb{R})\), and use them to prove directly that the process is Hölder (\(\frac{1}{2} - \delta \))-continuous for any \(\delta>0\).
reviewed by: Nasir N. Ganikhodjaev
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 6247830
zbMATH Keywords: \(\text{Airy}_1\) process
zbMATH Keywords: Fredholm determinant
zbMATH Keywords: Brownian motion
MaRDI profile type: Publication
OpenAlex ID: W1662384341
arXiv ID: 1201.4709
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DOI: 10.1007/S00440-012-0466-8
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 6247830