Domokos Szász - Selected Publications#

[1] Tail asymptotics of free path lengths for the periodic Lorentz process. On Dettmann's "Horizon" Conjectures. (with P. Nándori and T. Varjú; arXiv:1210.2231) pp. 30. (accepted by Communications Mathematical Physics with conclusion: "Thank you for submitting so interesting paper to CMP!")
[proof of Thm1 is an elementary coup de force; offering a program for future, too]

[2] Mixing rates of particle systems with energy exchange. Nonlinearity. 25:2349-2376, 2012, (with A. Grigo and K. Khanin)
[In the much successful heuristic physical strategy of heat conduction (aiming at deriving Fourier heat conduction law from microscopic principles; Gaspard-Gilbert, 2008-), this model serves as the first direct step toward its mathematically rigorous study]

[3] Limit Theorems for Perturbed Lorentz Processes. Duke Math. Journal. 148:459-499, 2009. (with D. Dolgopyat and T. Varjú)[solving, in particular, a 1981 problem of Sinai; basic idea of the proof comes from a 1981 work of Szász]

[4] Limit Laws and Recurrence for the Planar Lorentz Process with Infinite Horizon. J. Stat. Physics, 129:59-80, 2007 (with T. Varjú)[among others the very first rigorous proof for Bleher's 1992 analytic argument for super-diffusion]

[5] Local Limit Theorem and Recurrence for the Planar Lorentz Process, Ergodic Theory and Dynamical Systems, 24 (2004), 257-278 ( with T. Varjú)
[though by then recurrence had had two different proofs, the approach through local limit theorem, an outstanding result in itself, had, however, lead to a boost, cf. [4]]

[6] Multi-dimensional Semi-Dispersing Billiards: Singularities and the Fundamental Theorem, Annales Henri Poincaré, 3 (2002), 451-482 (with P. Bálint, N. Chernov, I. P. Tóth)
[for d > 2, the paper revealed a gap, overseen by every expert, in all proofs of the Fundamental Theorem; moreover, much importantly - by also using algebraic geometry, cf. [7] - it eliminated the gap for algebraic billiards thus saving the most important applications]

[7] Hard Ball Systems are Completely Hyperbolic, Ann. of Math. 149:35--96, 1999 (with N. Simányi)
[using - absolutely unexpectedly - algebraic-geometric methods, the work provided the first ever result on the hyperbolicity of any number of balls in any dimension; having pursued this approach Simányi could finally settle the Boltzmann-Sinai ergodic hypothesis in 2013]

[8] A `Transversal' Fundamental Theorem for Semi-Dispersing Billiards. Comm. Math. Phys. 129:535-560, 1990 (with A. Krámli and N. Simányi)

[9] The K-Property of Three Billiard Balls. Ann. of Math. 133:37--72, 1991 (with A. Krámli and N. Simányi)
[the very first breakthrough for proving Boltzmann-Sinai ergodic hypothesis for more than two balls]

[10] Towards a unified dynamical theory of the Brownian particle in an ideal gas. Comm. Math. Phys. 111:41--62, 1987. (with B. Tóth)
[the beautiful and hard results on the Rayleigh gas of this work closed a topic, vigorously investigated in the 80's. ]

CITATIONS:

A. Invited lecture of M. Sasada on XVIIth International Congress of Mathematical Physics (2012, Aalborg) is fully devoted to the model introduced in [2]], discusses in detail its results on the spectral gap, and characterization of reversible measures (http://www.icmp12.com/media/13809/title-abstract-(sasada).pdf).

B. Dolgopyat's invited talk on ICM06, Madrid discusses in very details three papers of Szász (cf. Chernov-Dolgopyat: Hyperbolic billiards and statistical physics, ICM06, Vol. II. 1679-1704). It also gives detailed ideas of a 1981 probabilistic work of Szász (in particular, these ideas got later used in the 2008, 2009 works of Dolgopyat, Szász and Varjú, (cf. [3] and its companion)). In the lecture, moreover, main results of the 2004 work [5] are contained in Theorems 1 and 2, and later the method of the same work is applied in a different place. The main statements of the 2007 work [4] are, in particular, repeated in Theorem 5.

C. From Sinai's comments (Selecta, 2010, Vol. I. p. 493): "Later in the works of D. Szász, N. Simányi and A. Krámli, the methods of this paper and previous papers were very deeply developed and gave the possibility to prove ergodicity and mixing in systems of N hard disks and balls (see many excellent papers related to the subject in the book edited by D. Szász [Sz1] ...)..." (N. B. Sinai refers among others to [7], [8], [9] and finally to Springer EMS101 (Hard Ball Systems and the Lorentz Gas) edited by Szász (this latter got also most highly praised by the review in UK Nonlinear News 7.5.2002))

D. In the bibliographies of fundamental monographs on different topics Szász's works are extensively cited (e. g. Chernov-Markarian: Chaotic Billiards, AMS, 2006 cites 7 papers, Spohn: Large Scale Dynamics of Interacting Particles, Springer, 1991 on dynamical theory of Brownian motion and hydrodynamics cites 8 papers of Szász).