Publication List
Preprints and submitted papers:
T. Bothner, A. Little, The complex elliptic Ginibre ensemble at weak non-Hermiticity: edge spacing distributions, https://arxiv.org/pdf/2208.04684.pdf, to appear in Random Matrices: Theory and Applications
Published research:
T. Bothner, A. Little, The complex elliptic Ginibre ensemble at weak non-Hermiticity: bulk spacing distributions, J. Phys. A: Mathematical and Theoretical (2024), doi:10.1088/1751-8121/ad508b
T. Bothner, A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: Scalar-valued kernels, Journal of Functional Analysis (2023), doi:10.1016/j/fa/2023./110160
T. Bothner, M. Cafasso, S. Tarricone, Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel, Ann. Inst. H. Poincare Probab. Statist. (2022), doi:10.1214/21-AIHP1211
J. Baik, T. Bothner, Edge distribution of thinned real eigenvalues in the real Ginibre ensemble, Annales Henri Poincare (2022), doi:10.1007/s00023-022-01182-0
T. Bothner, On the origins of Riemann-Hilbert problems in mathematics, Nonlinearity 34 (2021), R1-R73
J. Baik, T. Bothner, The largest real eigenvalue in the real Ginibre ensemble and its relation to the Zakharov-Shabat system, Ann. Appl. Probab. (2020), Vol. 30, No. 1, 460-501
T. Bothner, P. Miller, Rational solutions of the Painleve-III equation: Large parameter asymptotics, Constructive Approximation (2019), doi:10.1007/s00365-019-09563-4
T. Bothner, A. Its, A. Prokhorov, On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential, Advances in Mathematics (2019) Vol. 345, 483-551
T. Bothner, W. Warner, Short distance asymptotics for a generalized two-point scaling function in the two-dimensional Ising model, Math Phys Anal Geom (2018) 21:37, doi: 10.1007/s11040-018-9296-y
T. Bothner, P. Miller, Y. Sheng, Rational solutions of the Painleve-III equation, Studies in Appl. Math. DOI: 10.11 11/sapm.12220 (2018) 141:626-679
T. Bothner, P. Deift, A. Its, I. Krasovsky, The sine process under the influence of a varying potential, Journal of Math. Phys. 59, 091414 (2018), doi: 10.1063/1.505039
T. Bothner, R. Buckingham, Large deformations of the Tracy-Widom distribution I. Non-oscillatory asymptotics, Commun. Math. Phys. 359 (2018), 223-263
T. Bothner, A short note on the scaling function constant problem in the two-dimensional Ising model, Journal of Statistical Physics 170 (4) (2018), 672-683
T. Bothner, P. Deift, A. Its, I. Krasovsky, On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II, Operator Theory: Advances and Applications 259 (2017), 213-234
T. Bothner, Transition asymptotics for the Painlev\'e II transcendent, Duke Mathematical Journal 166 (2017), 205-324
F. Balogh, M. Bertola, T. Bothner, Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials, Constructive Approximation 44 (2016), 417-453
T. Bothner, From gap probabilities in random matrix theory to eigenvalue expansions, J. Phys. A: Mathematical and Theoretical 49 (2016) 075204 (77p)
T. Bothner, P. Deift, A. Its, I. Krasovsky, On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential I, Commun. Math. Phys. 337 (2015), 1397-1463
M. Bertola, T. Bothner, Universality conjecture and results for a model of several coupled positive-definite matrices, Commun. Math. Phys. 337 (2015), 1077-1141
M. Bertola, T. Bothner, Zeros of large degree Vorob'ev-Yablonski polynomials via a Hankel determinant identity, Int. Math. Research Notices DOI:10.1093/imrn/rnu239 (2014)
P. Bleher, T. Bothner, Calculation of the constant factor in the six-vertex model, Ann. Inst. Henri Poincare Comb. Phys. Interact 1 (2014), 363-427
T. Bothner, A. Its, Asymptotics of a cubic sine kernel determinant, St. Petersburg Math. J. 26 (2014), 22-92
T. Bothner, A. Its, Asymptotics of Fredholm determinant corresponding to the first bulk critical universality class in random matrix models, Commun. Math. Phys. 328 (2014), 155-202
T. Bothner, K. Liechty, Tail decay for the distribution of the endpoint of a directed polymer, Nonlinearity 26 (2013), 1449-1472
P. Bleher, T. Bothner, Exact solution of the six-vertex model with domain wall boundary conditions. Critical line between disordered and antiferroelectric phases, Random Matrices: Theory and Applications DOI:10.1142/S2010326312500128 (2012)
T. Bothner, A. Its, The nonlinear steepest descent approach to the singular asymptotics of the second Painlev\'e transcendent, Physica D 241 (2012), 2204-2225
W. Balser, T. Bothner, Computation of formal solutions of linear systems of difference equation, Advances in Dynamical Systems and Applications 5 (2010), 29-47