Obituary: Professor Roland Dobrushin

Roland Dobrushin was one of the most brilliant representatives of the Russian school of probability theory founded by Andrei Kolmogorov.

It was not until after 1945 that the impact of the Russian probabilists' work was felt significantly. For more than two decades a relatively small team of young researchers (often undergraduates), grouped around Kolmogorov and Eugene Dynkin in Moscow, and later around Yuri Linnik in what was then Leningrad, was unchallenged in the vast area of theoretical and applied mathematics related to the concept of probability. It was an example of the tremendous success which could be achieved by a community not only inspired by the internal beauty of their abstract subject, but united in working in the specific social and political atmosphere of a country relatively isolated from the rest of the world.

From the 1950s onwards, probabilists, both Soviet and Western, gradually moved from theoretical towards more applied subjects. The importance of research in those areas where a probabilistic approach seemed promising did not escape the notice of the superpowers. Two notable examples of these applied areas are information theory and mathematical physics. The consequences were dramatic: from being collections of loosely connected facts of an empirical nature, these disciplines became integral parts of probability theory. Probabilistic language and, more importantly, a probabilistic way of thinking, provided them with a logical framework which both disciplines had previously lacked, and made possible spectacular progress throughout the 1970s and 1980s.

Dobrushin played a key role in the process of integration. In addition to his probabilistic intuition (the joke ran that he understood the notion of expected value better than anyone in the world), and superb analytical techniques, he possessed to an exceptional degree the ability to convert phenomenological and half-intuitive arguments used by applied mathematicians and others into fine mathematical statements.

In the area of information theory he proved, in 1960, a general form of Claud Shannon's theorems (which establish the limits of the speed with which information can be sent through a channel) and made important contributions to coding theory. In mathematical physics, he gave in 1965 a general definition of a Gibbs state (later known as a Dobrushin- Lanford-Ruelle or DLR state) which provided the perfect foundation for the concept of phase transition - the instantaneous passage from one state of matter (say, a gaseous one to a liquid one) - a definition which had hitherto eluded many outstanding specialists in the field. He then gave a beautiful proof of the existence of phase transition in the famous Ising model. The central part of this proof was the so-called Peierls' argument, named after Sir Rudolf Peierls, sometime Wykeham Professor of Physics at Oxford, who predeceased Dobrushin by only a few weeks.

Using his definition of a Gibbs state, and with the help of Peierls' argument, Dobrushin proved in a few lines that in the Ising model there exists a unique Gibbs state for high temperatures, and many such states for low temperatures and zero magnetic field. In other words, there is no phase transition for high temperatures but there is one for low temperatures. This discovery resulted in a complete revision of the whole theory of phase transitions to which Dobrushin, with other authors, contributed many fine ideas and arguments.

Roland Dobrushin will be remembered as an outstanding mathematician, and as an extraordinary personality. A man of strong character and great personal integrity, he quickly found himself at odds with the officialdom of the Soviet system. In 1959 at a meeting in the Department of Mechanics and Mathematics at Moscow State University (Mekh-mat), he denounced an official point of view. He was rebuked by the local Communist Party authorities, and his career at Mekh-mat was blocked. He was prevented from defending his doctoral thesis at Moscow University (although he finally managed to obtain a degree elsewhere), and his upgrading was turned down by the Mekh-mat Communist Party organisation. His case was generally considered as one of the first examples of repressive measures carried out against Soviet mathematicians.

Notwithstanding, Dobrushin continued defying the authorities. He was a co-signatory in the 1960s of many protest letters denouncing political trials (such as the Sinyavskii-Daniel trial) and other reprisals against the growing dissident movement. He resigned from Mekh-mat in 1965, thereby setting an example for the many top-class mathematicians and physicists who, voluntarily or involuntarily, left Moscow State University, unable to live under the increasing pressure from apparatchiks.

Dobruchin was appointed as Head of Laboratory at the Moscow Institute for Problems of Information Transmission, part of the Soviet Academy of Sciences. The atmosphere in many research institutes of the Academy was far more liberal: leading dissidents such as Andrei Sakharov enjoyed the support and loyalty of colleagues, and the administration even offered some protection, within limits, to those members of staff looked on with disfavour by the Communist Party and the Soviet authorities. This was in part due to the long tradition of relative freedom allowed to those physicists and mathematicians who had in some way contributed to the Soviet nuclear and space programmes.

Dobrushin was fortunate to have found a position in such an institute, where throughout the 1960s and 1970s he formed an active group of researchers which distinguished itself in several fields of mathematics. One of his recruits was awarded the Fields Medal, a prestigious award of the International Union of Mathematicians; another was awarded the Medal of the European Union of Mathematics. His laboratory became a Mecca for visitors from around the world.

Such visits helped to maintain a regular exchange of ideas between researchers on both sides of the Iron Curtain. To the annoyance of the authorities, these exchanges were not of a purely mathematical nature: helping dissidents and refusniks (those who had applied for, and been refused, permission to leave the Soviet Union) was one of his primary concerns - although he never formally associated himself with any dissident group, nor considered leaving his country.

There was, however, one aspect of professional life where officialdom had the upper hand: election to Academician. There was no chance of such an election by the conservative Mathematics Section of the Academy, partly because of Dobrushin's anti-authority stance, but also because of his non-Russian origins. He came from a prominent Jewish family, his uncle being a member of the Jewish Committee active in the disclosure of Nazi atrocities during the Second World War. After the war, all the committee members and many other Jewish activists were sentenced to labour camps which few survived. Nor did Dobrushin's German background (immigrants to St Petersburg, where he was born in 1929) find favour with the Academy purists.

Dobrushin never himself sought election. Many years later, in 1991, another outstanding mathematician, who had similarly been denied the honour, was finally elected. In his speech of congratulation on that occasion, Dobrushin said: "The fact that you have been elected does not change my opinion of you, but does change my opinion of the Academy."

A second aspect of life which the authorities could control was travel outside the Soviet Union. Dobrushin's enormous popularity, both professionally and personally, resulted in numerous invitations and honours. In 1982, together with Iris Murdoch, he was elected Honorary Member of the American Academy of Fine Arts and Sciences in Boston, but was unable to attend the presentation. It was not until 1988, with glasnost and perestroika, that he was finally given permission to travel abroad. Even then, such was the inertia of the whole cumbrous system that it required the intervention of a member of Gorbachev's inner circle before his visa was granted.

This long-awaited freedom was greeted with great enthusiasm by his Western colleagues. At last he visited the United Kingdom. On his second trip, in 1993, he spent several months at the Isaac Newton College Institute of Cambridge University. He then travelled to Oxford to meet Peierls for the first and only time, over lunch in New College.

Roland Dobrushin will be remembered as a torch-bearer in many flourishing areas of theoretical and applied research. A popular joke at gatherings of Moscow mathematicians and physicists concerned a man who drops a valuable item in the dark, and undertakes an intensive search for it a few steps away, under a street light. A bystander asks him why he does not conduct his search where he dropped the item, to which the man replies that his only chance of finding it is under the light: the moral being, take care where you put street lights! Dobrushin was a striking example of a man who intuitively knew where the light, in the form of new definitions and related ideas, should be put.

Dobrushin was a great bear of a man, with a huge smile and wonderful sense of humour, who was much loved and admired by his many friends. Despite his unathletic appearance, he possessed remarkable physical stamina, and he greatly enjoyed (like so many Russians) swimming, and alpine and cross- country skiing expeditions. Once in the 1960s, with other prominent young mathematicians, he was hiking in a mountainous region of Central Asia. It was difficult terrain and one of the group was injured, despite his superior expertise and training. Dobrushin, in sympathy, said: "Forgive me - I know it is I who ought to have fallen, not you."

Yuri Suhov

Roland L'vovich Dobrushin, mathematician: born Leningrad 29 July 1929; Assistant Professor, Department of Mechanics and Mathematics, Moscow State University 1955-65, Professor 1991-95; Head of Laboratory, Institute of Problems Transmission, Russian Academy of Sciences 1965-95; married four times (five daughters); died Moscow 12 November 1995.