# Domokos Szász

### Born: 18 August 1941 in Budapest, Hungary

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**Domokos Szász**was brought up and educated in Budapest. After graduating from high school in 1959, he entered the Faculty of Sciences of the Eötvös Loránd University in Budapest where he was attracted to probability theory. He graduated in 1964 with a Diploma in Mathematics and continued to study at Eötvös Loránd University where he was appointed as an Assistant Professor in the Probability Department. His first publication

*On the general branching process with continuous time parameter*was published in 1967. Joseph Doob explains that in this paper Szász:-

Also in 1967, he was awarded his second degree, the Dr. rer. nat, for his graduate thesis... gives a systematic presentation of general continuous parameter branching processes. Application is made to find under what kind of branching a Poisson random point distribution remains one.

*Spreading processes*(Hungarian). He continued to work at Eötvös Loránd University until 1968 when he went to Moscow to study for his Candidate's Degree at the Lomonosov University of Moscow. There his thesis advisor was Boris Vladimirovich Gnedenko, but he was also strongly influenced by Roland Lvovich Dobrushin and by Yakov Grigorevich Sinai, both of whom had been students of Andrey Nikolaevich Kolmogorov.

In 1969 Szász received the Géza Grünwald Commemorative Prize from the János Bolyai Mathematical Society, an award given to outstanding young mathematicians. He was awarded his Candidate's degree (with distinction) from the Lomonosov University of Moscow in 1971 for his thesis

*The asymptotic behaviour of sums of a random number of independent random variables*(Russian). This was a highly productive time for Szász who published six papers in 1971, one in English, two in Hungarian and three in Russian. Szász was appointed to the Mathematical Institute of the Hungarian Academy of Sciences in 1971. He held this position until 1999. He was awarded a doctorate (equivalent to a D.Sc. or habilitation) in 1981 for his thesis

*Random point distributions and their applications in reliability theory and statistical physics*(Hungarian). In [2] he explains the main thrusts of his research:-

In 1984 he received the Research Prize of the Hungarian Academy of Sciences and in 1990 he was elected as a Corresponding Member of the Hungarian Academy of Sciences being elected an Ordinary Member five years later. Also in 1995 he was awarded the Tibor Szele Prize by the János Bolyai Mathematical Society. This award is given to leading researchers who have founded important scientific schools. He has been invited as a visiting professor to a number of universities: Dartmouth College, USA (6 months in 1977), Goethe University, Frankfurt (6 months in 1977-78), Dartmouth College, USA (6 months in 1985), and Princeton University, USA (1990-91).My encounter with the Moscow mathematical school, in particular with Dobrushin and Sinai and their students, turned my interest in the mid1970's to mathematical statistical physics and later to dynamical systems, both in an enthralling blossoming then and since. Starting with the early1980's I have been thinking a lot on ergodic and stochastic properties of hard ball systems and billiards, and of hyperbolic dynamical systems with singularities, in general. Central questions have been how to establish the Boltzmann-Sinai Ergodic Hypothesis and how to prove probabilistically or statistical physically interesting properties of these systems. I am also much interested in the dynamical theory of Brownian motion. I could convince several clever guys in Budapest, how attractive mathematical statistical physics and dynamical systems are.

In 1999 he was made Director of Mathematical Institute of the Budapest University of Technology and Economics. In 2000 he became Distinguished Széchenyi Professor at the Budapest University of Technology and Economics. He was awarded the Széchenyi Prize in 2005, an award made by the Hungarian State to those who have made an outstanding contribution to academic life in Hungary. The prize was presented to Szász on National Day (15 March) by Ferenc Mádl, the President of Hungary.

Let us look briefly at a couple of the problems to which Szász has made major contributions. One is the Boltzmann-Sinai conjecture and we quote Nikolai Chernov's comments on the history of the problem in his review of the paper

*Hard ball systems are completely hyperbolic*(1999) by Szász and Nándor Simányi:-

The Lorentz system describes the motion of a free point particle which is reflected from the boundaries of a convex scatterer. Szász, working with different co-investigators, examined the recurrence of such a system when there is a periodic configuration of scatterers. In a 1985 paperThe paper presents a partial solution of a classical open problem in mathematical physics, which is to prove rigorously the ergodicity of a system consisting of any number of identical hard balls in a box with periodic boundary conditions(i.e., on a torus). This problem is ascribed to a hypothesis stated by L Boltzmann more than a hundred years ago. A rigorous version of this hypothesis is due to Ya A Sinai, who proved it for two balls in1970and made several crucial contributions to the study of the problem later, from1973to1987, including the proof of the so-called "fundamental theorem in the theory of dispersing billiards". Sinai's seminal paper in1970opened the door to a new branch of mathematical physics - the theory of hyperbolic(chaotic)billiard systems. The Boltzmann-Sinai conjecture was proved for three balls in1991by A Krámli, N Simányi and D Szász. The next year the same authors proved the conjecture for four balls. Under certain additional restrictions on the dimension of the balls or the graph of allowable collisions, the conjecture was proved for larger numbers of balls. This paper establishes the complete hyperbolicity of a system of any number of hard balls on a torus. The only restriction is that the masses of the balls must be "generic", i.e. avoid some exceptional submanifolds of codimension one. ... The proof is based on fascinating constructions.

*The problem of recurrence for Lorentz processes*with András Krámli he proved a weak form of recurrence while in

*Local limit theorem for the Lorentz process and its recurrence in the plane*(2004) written with Tamás Varjú they proved strong recurrence properties. This work is related to that done by Lai-Sang Young.

Szász married in 1975 and has a daughter and two sons.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (4 books/articles)

**Mathematicians born in the same country**

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