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pro vyhledávání: '"Thomas Bothner"'
Autor:
Thomas Bothner
Publikováno v:
Bothner, T 2021, ' On the origins of Riemann-Hilbert problems in mathematics ', Nonlinearity, vol. 34, no. 4, pp. R1-R73 . https://doi.org/10.1088/1361-6544/abb543
This article is firstly a historic review of the theory of Riemann-Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert's 21st problem and Plemelj's work associated with it. The secondary purpose of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4c2df7aeebfe95547246386b0c11861
https://hdl.handle.net/1983/390124cd-f079-4158-8afe-6700a4b905fc
https://hdl.handle.net/1983/390124cd-f079-4158-8afe-6700a4b905fc
Publikováno v:
Bothner, T, Cafasso, M & Tarricone, S 2022, ' Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel ', Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, vol. 58, no. 3, pp. 1505–1546 . https://doi.org/10.1214/21-AIHP1211
We rigorously compute the integrable system for the limiting $(N\rightarrow\infty)$ distribution function of the extreme momentum of $N$ noninteracting fermions when confined to an anharmonic trap $V(q)=q^{2n}$ for $n\in\mathbb{Z}_{\geq 1}$ at positi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f61ecdc1c73577c33c2abb4da55a96f8
https://hal.archives-ouvertes.fr/hal-03115038
https://hal.archives-ouvertes.fr/hal-03115038
Autor:
Thomas Bothner, Jinho Baik
Publikováno v:
Ann. Appl. Probab. 30, no. 1 (2020), 460-501
Baik, J & Bothner, T 2020, ' The largest real eigenvalue in the real Ginibre ensemble and its relation to the Zakharov–Shabat system ', Annals of Applied Probability, vol. 30, no. 1, pp. 460-501 . https://doi.org/10.1214/19-aap1509
Baik, J & Bothner, T 2020, ' The largest real eigenvalue in the real Ginibre ensemble and its relation to the Zakharov–Shabat system ', Annals of Applied Probability, vol. 30, no. 1, pp. 460-501 . https://doi.org/10.1214/19-aap1509
The real Ginibre ensemble consists of $n\times n$ real matrices ${\bf X}$ whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attai
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a7c4535a1410e5abb88c03f1ce9731e
https://projecteuclid.org/euclid.aoap/1582621229
https://projecteuclid.org/euclid.aoap/1582621229
Autor:
Peter D. Miller, Thomas Bothner
Publikováno v:
Bothner, T & Miller, P D 2020, ' Rational Solutions of the Painlevé-III Equation : Large Parameter Asymptotics ', CONSTRUCTIVE APPROXIMATION, vol. 51, no. 1, pp. 123-224 . https://doi.org/10.1007/s00365-019-09463-4
Bothner, T & Miller, P D 2020, ' Rational Solutions of the Painlevé-III Equation : Large Parameter Asymptotics ', Constructive Approximation, vol. 51, no. 1, pp. 123-224 . https://doi.org/10.1007/s00365-019-09463-4
Bothner, T & Miller, P D 2020, ' Rational Solutions of the Painlevé-III Equation : Large Parameter Asymptotics ', Constructive Approximation, vol. 51, no. 1, pp. 123-224 . https://doi.org/10.1007/s00365-019-09463-4
The Painlevé-III equation with parameters Θ = n+ m and Θ ∞= m- n+ 1 has a unique rational solution u(x) = u n(x; m) with u n(∞; m) = 1 whenever n∈ Z. Using a Riemann–Hilbert representation proposed in Bothner et al. (Stud Appl Math 141:626
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e039acf8b9f17e5c44d406d7a2d7e0d
https://kclpure.kcl.ac.uk/en/publications/698bb619-52e1-4ddc-b010-70716b3a05a2
https://kclpure.kcl.ac.uk/en/publications/698bb619-52e1-4ddc-b010-70716b3a05a2
Publikováno v:
Bothner, T, Miller, P D & Sheng, Y 2018, ' Rational Solutions of the Painlevé-III Equation ', Studies in Applied Mathematics, pp. 626-679 . https://doi.org/10.1111/sapm.12220
Bothner, T J, Miller, P D & Sheng, Y 2018, ' Rational Solutions of the Painlevé-III Equation ', STUDIES IN APPLIED MATHEMATICS, vol. 141, no. 4, pp. 626-679 . https://doi.org/10.1111/sapm.12220
Bothner, T J, Miller, P D & Sheng, Y 2018, ' Rational Solutions of the Painlevé-III Equation ', STUDIES IN APPLIED MATHEMATICS, vol. 141, no. 4, pp. 626-679 . https://doi.org/10.1111/sapm.12220
All of the six Painlev´e equations except the first have families of rationalsolutions, which are frequently important in applications. The third Painlev´eequation in generic form depends on two parameters m and n, and it has rational solutions if
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b9f0b67b77978d8aadce492d55a0bf6
https://doi.org/10.1111/sapm.12220
https://doi.org/10.1111/sapm.12220
Autor:
Thomas Bothner
Publikováno v:
Bothner, T 2018, ' A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model ', Journal of Statistical Physics, vol. 170, no. 4, pp. 672-683 . https://doi.org/10.1007/s10955-017-1947-z
We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the $2$-point function of the two-dimensional Ising model. This factor was first computed by C. Tracy in \cite{T} via an expon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9583e9efbfe0a0ad1fe0ec2617b71533
https://doi.org/10.1007/s10955-017-1947-z
https://doi.org/10.1007/s10955-017-1947-z
Autor:
Jinho Baik, Thomas Bothner
Publikováno v:
Baik, J & Bothner, T 2022, ' Edge distribution of thinned real eigenvalues in the real Ginibre ensemble ', Annales Henri Poincaré, vol. 23, no. 11, pp. 4003-4056 . https://doi.org/10.1007/s00023-022-01182-0
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed independently with constant likelihood. We show that th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f57c487ee548d61e76ca4c3bba2607a5
Autor:
Thomas Bothner, William Warner
Publikováno v:
Bothner, T J & Warner, W 2018, ' Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model ', Mathematical Physics, Analysis and Geometry . https://doi.org/10.1007/s11040-018-9296-y
Bothner, T & Warner, W 2018, ' Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model ', Mathematical Physics, Analysis and Geometry, vol. 21, 37 (2018) . https://doi.org/10.1007/s11040-018-9296-y
Bothner, T & Warner, W 2018, ' Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model ', Mathematical Physics, Analysis and Geometry, vol. 21, 37 (2018) . https://doi.org/10.1007/s11040-018-9296-y
In the 1977 paper \cite{MTW} of B. McCoy, C. Tracy and T. Wu it was shown that the limiting two-point correlation function in the two-dimensional Ising model is related to a second order nonlinear Painlev\'e function. This result identified the scali
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d182f5acf2f00d575310cd9a62ec81e1
https://kclpure.kcl.ac.uk/ws/files/103731104/Short_Distance_Asymptotics_BOTHNER_Accepted_21_Nov_18_GOLD_VoR_CC_BY.pdf
https://kclpure.kcl.ac.uk/ws/files/103731104/Short_Distance_Asymptotics_BOTHNER_Accepted_21_Nov_18_GOLD_VoR_CC_BY.pdf
Publikováno v:
Bothner, T, Deift, P, Its, A & Krasovsky, I 2018, ' The sine process under the influence of a varying potential ', Journal of Mathematical Physics, vol. 59, no. 9, 091414 . https://doi.org/10.1063/1.5050394
We review the authors' recent work \cite{BDIK1,BDIK2,BDIK3} where we obtain the uniform large $s$ asymptotics for the Fredholm determinant $D(s,\gamma):=\det(I-\gamma K_s\upharpoonright_{L^2(-1,1)})$, $0\leq\gamma\leq 1$. The operator $K_s$ acts with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12b1069344a6f61f2067beacead2a8a2
http://arxiv.org/abs/1807.11387
http://arxiv.org/abs/1807.11387
Autor:
Thomas Bothner, Marco Bertola
Publikováno v:
Communications in Mathematical Physics. 337:1077-1141
The paper contains two main parts: in the first part, we analyze the general case of $p\geq 2$ matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain form a mu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c585717bbcf355978a9ddb9965c214d
https://doi.org/10.1007/s00220-015-2327-7
https://doi.org/10.1007/s00220-015-2327-7