Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function
By Jinho Baik, Robert Buckingham, J. DiFranco. 2007
165 citations recorded by the source corpus.
The Tracy-Widom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first is the evaluation of the total integral of the Hastings-McLeod solution of the Painlevé II equation. The second is the evaluation of the constant term of the asymptotic expansions of the Tracy-Widom distribution functions as the distribution parameter approaches minus infinity. For the GUE Tracy-Widom distribution function, this gives an alternative proof of the recent work of Deift, Its, and Krasovsky. The constant terms for the GOE and GSE Tracy-Widom distribution functions are new.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/abde4b5561630331c265403f67468a2f509f0e10
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In Management Science and Operations Research
In Statistics and Probability
- B'alint Vir'ag
- Brian Rider
- A. Nahum
- G. Schehr
- Arnab K. Pal
- Harold Widom
- Craig A. Tracy
- Satya N. Majumdar
Citations in the corpus
- Beta ensembles, stochastic Airy spectrum, and a diffusion (2006, background): “(In fact, for β = 1, 2, 4 these type of asymptotics are known down to the constant order terms; see for example [3].”
- Higher‐order analogues of the Tracy‐Widom distribution and the Painlevé II hierarchy (2009, background): “26) was given recently in [17] and another proof followed shortly in [2].”
- The Distributions of Random Matrix Theory and their Applications (2009, background): “We quote the final results and refer the reader to [3] for a history of this problem.”
- Extreme value statistics of correlated random variables: A pedagogical review (2019, methodology): “[183–185] and [186, 187] for more precise asymptotics of the left and right tail of the β-TW distribution respectively.”
- Stochastic resetting and applications (2019, background): “In particular, f1(χ) has asymmetric non-Gaussian tails [136, 137]:”
- Operator Spreading in Random Unitary Circuits (2017, background): “The former asymptotic expansion of F2 was achieved only recently [106,107].”