ISSN 0032-9460, Problems of Information Transmission, 2009, Vol. 45, No. 4, pp. 406–409.
Pleiades Publishing, Inc., 2009.
Original Russian Text
the Editorial Board, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 4, pp. 120–124.
The International Dobrushin Prize
The International Dobrushin Prize for 2009 was awarded to Yakov Grigor’evich Sinai. Sinai is
aﬃliated with the Landau Institute for Theoretical Physics of the Russian Academy of Sciences and
the Mathematics Department of Princeton University. The prize was presented on July 16, 2009,
at the conference in honor of the 80th anniversary since the birth of Roland L’vovich Dobrushin.
Yakov Sinai’s Lecture
Nonstandard Ergodic Theorems for Unbounded Functions
Roland L’vovich Dobrushin was one of the best probabilists of our generation. He had remark-
able probabilistic intuition that allowed him to obtain an answer in almost any situation without yet
having a rigorous proof. Dobrushin was a student of A.N. Kolmogorov, whom he esteemed and re-
spected greatly, and Kolmogorov always endeavored to attend Dobrushin’s scientiﬁc presentations.
Throughout his life Dobrushin also maintained a close relationship with E.B. Dynkin.
Dobrushin started his scientiﬁc career at the time when the famous books of W. Feller on
probability theory and J.L. Doob on the theory of random processes were published in Russian.
Doob’s book contained a cumbersome construction of separable processes that did not satisfy
many probabilists. Dobrushin understood all the aspects of this theory very well. At some point
I.M. Gelfand decided to study the theory of random processes and invited Dobrushin for this
purpose. The result of these lectures was Gelfand’s well-known work that laid out the foundation
of the theory of generalized random processes. Around the same time the work of the prominent
Japanese mathematician K. Itˆo on the same topic appeared. The well-known works of R.A. Minlos
on the conditions for σ-additivity of measures on function spaces were also written around this
Dobrushin’s PhD dissertation was devoted to the description of all limiting distributions for
two-state Markov chains. This work fully revealed Dobrushin’s probabilistic intuition. Later he
turned to information theory, and this was the subject of his doctoral dissertation. However,
soon thereafter Dobrushin became less interested in classical probability theory. During a Vilnius
conference he gave a talk in which he claimed that there were no interesting problems remaining
in probability theory. With this he alienated many of those working in classical probability theory.
However, this did not hurt him very much. On the one hand, he was already an eminent ﬁgure in
this ﬁeld. On the other hand, Dobrushin had the reputation of an “enfante terrible,” and in this
case it worked in his favor to some extent. A positive result of this talk was that Dobrushin began
collaborating with Minlos and they decided to study statistical physics together. They invited me
to collaborate with them also, but I decided only to attend the discussions at ﬁrst. At that time
I was leading a seminar on the theory of dynamical systems, attended by many young talented
mathematicians, some of whom are participating in this conference today.
At ﬁrst we studied general theorems of Van Hove type (which is a rather boring but unavoidable
topic). The situation changed after Dobrushin carried out his remarkable work on phase transitions
in ferromagnetic Ising models. He showed that at low temperatures the probability distribution