Keywords: logarithmic gas, partition function.
@article{TMF_2023_216_2_a1,
author = {A. V. Zabrodin},
title = {Dyson diffusion on a~curved contour},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {226--233},
year = {2023},
volume = {216},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a1/}
}
A. V. Zabrodin. Dyson diffusion on a curved contour. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 226-233. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a1/
[1] F. J. Dyson, “A Brownian-motion model for the eigenvalues of a random matrix”, J. Math. Phys., 3:6 (1962), 1191–1198 | DOI | MR
[2] F. J. Dyson, “Statistical theory of the energy levels of complex systems. I”, J. Math. Phys., 3:1 (1962), 140–156 ; “Statistical theory of the energy levels of complex systems. II”, 157–165 | DOI | MR | DOI
[3] P. J. Forrester, Log-Gases and Random Matrices, London Mathematical Society Monographs Series, 34, Princeton Univ. Press, Princeton, 2010 | DOI | MR
[4] P. Wiegmann, A. Zabrodin, “Dyson gas on a curved contour”, J. Phys. A: Math. Theor., 55:16 (2022), 165202, 34 pp. | DOI | MR
[5] F. C. Klebaner, Introduction to Stochastic Calculus and Applications, Imperial College Press, London, 1998 | MR
[6] B. Oksendal, Stokhasticheskie differentsialnye uravneniya. Vvedenie v teoriyu i prilozheniya, Mir, AST, M., 2003 | DOI | MR
[7] B. Jancovici, “Classical Coulomb systems: Screening and correlations revisited”, J. Stat. Phys., 80 (1995), 445–459 | DOI
[8] P. Wiegmann, A. Zabrodin, “Large scale correlations in normal non-Hermitian matrix ensembles”, J. Phys. A: Math. Gen., 36:12 (2003), 3411–3424 | DOI | MR
[9] P. Wiegmann, A. Zabrodin, “Large $N$ expansion for normal and complex matrix ensembles”, Frontiers in Number Theory, Physics and Geometry. I, eds. P. Cartier, B. Julia, P. Moussa, P. Vanhove, Springer, Berlin, 2006, 213–229 | MR
[10] A. Zabrodin, P. Wiegmann, “Large $N$ expansion for the 2D Dyson gas”, J. Phys. A: Math. Gen., 39:28 (2006), 8933–8964 | DOI | MR
[11] A. Zabrodin, “Matrix models and growth processes: from viscous flows to the quantum Hall effect”, Applications of Random Matrices in Physics, NATO Science Series II: Mathematics, Physics and Chemistry Mathematics, Physics and Chemistry, 221, eds. É. Brézin, V. Kazakov, D. Serban, P. Wiegmann, A. Zabrodin, Springer, Dordrecht, 2006, 261–318, arXiv: hep-th/0412219 | DOI | MR
[12] K. Johansson, Strong Szegő theorem on a Jordan curve, arXiv: 2110.11032
[13] Y. Wang, “Equivalent descriptions of the Loewner energy”, Invent. Math., 218:2 (2019), 573–621 | DOI | MR
[14] Y. Wang, “Large deviations of Schramm–Loewner evolutions: A survey”, Probab. Surv., 19 (2022), 351–403 | DOI | MR
[15] L. Takhtajan, L.-P. Teo, “Kähler potential and period mapping”, Weil–Petersson Metric on the Universal Teichmüller Space, Chapter 2, Memoirs of the American Mathematical Society, 183, No 861, AMS, Providence, RI, 2006, arXiv: math/0406408 | DOI | MR