Infinite dimensional stochastic differential equations for Dyson’s model
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Anderson, G.W., Guionnet, A., Zeitouni, O.: An introduction to random matrices, vol. 118. Cambridge University Press, Cambridge (2010)
Cépa, E.: Équations différentielles stochastiques multivoques. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds.) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, pp. 86–107. Springer, Berlin, Heidelberg (1995). doi:10.1007/BFb0094202
Corwin, I.: The Kardar-Parisi-Zhang equation and universality class. Random Matrices Theory Appl. 1(1), 1130001 (2012). doi:10.1142/S2010326311300014
Corwin, I., Hammond, A.: Brownian Gibbs property for Airy line ensembles. Invent. Math. 195(2), 441–508 (2014)
Corwin, I., Hammond, A.: KPZ line ensemble. Probab. Theory Relat. Fields (2015). doi:10.1007/s00440-015-0651-7
Dyson, F.J.: A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys. 3(6), 1191–1198 (1962)
Gorin, V., Shkolnikov, M.: Interacting particle systems at the edge of multilevel Dyson Brownian motions. (2014). arXiv:1409.2016
Gorin, V., Shkolnikov, M.: Multilevel Dyson Brownian motions via Jack polynomials. Probab. Theory Relat. Fields pp. 1-51 (2014)
Karatzas, I., Shreve, S.: Brownian motion and Stochastic calculus (Graduate Texts in Mathematics), vol. 113. Springer (1991)
Katori, M., Tanemura, H.: Zeros of airy function and relaxation process. J. Stat. Phys. 136(6), 1177–1204 (2009)
Katori, M., Tanemura, H.: Non-equilibrium dynamics of Dyson’s model with an infinite number of particles. Commun. Math. Phys. 293(2), 469–497 (2010)
Lang, R.: Unendlich-dimensionale Wienerprozesse mit wechselwirkung. I. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 38(1), 55–72 (1977)
Lang, R.: Unendlich-dimensionale Wienerprozesse mit wechselwirkung. II. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 39(4), 277–299 (1977)
McKean, H.P.: Stochastic integrals, vol. 353. American Mathematical Soc., Providence (1969)
Mehta, M.L.: Random matrices, vol. 142. Academic Press (2004)
Osada, H.: Infinite-dimensional stochastic differential equations related to random matrices. Probab. Theory Relat. Fields 153(3–4), 471–509 (2012)
Osada, H.: Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials. Ann. Probab. 41(1), 1–49 (2013)
Osada, H.: Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: airy random point field. Stoch. Process. Appl. 123(3), 813–838 (2013)
Osada, H., Tanemura, H.: Infinite-dimensional stochastic differential equations and tail $$\sigma $$-fields. (2014). arXiv:1412.8674
Osada, H., Tanemura, H.: Infinite-dimensional stochastic differential equations arising from Airy random point fields. (2014). arXiv:1408.0632
Osada, H., Tanemura, H.: Strong Markov property of determinantal processes with extended kernels. (2014). arXiv:1412.8678
Spohn, H.: Interacting Brownian particles: a study of Dyson’s model. In: Hydrodynamic behavior and interacting particle systems, pp. 151-179. Springer (1987)
