mathematics

Roland Dobrushin

Roland Dobrushin is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Roland Dobrushin rather than just read about it. In short: Roland Lvovich Dobrushin (Russian: Рола́нд Льво́вич Добру́шин) (July 20, 1929 – November 12, 1995) was a mathematician who made important contributions to probability theory, mathematical physics, and information theory. Life and work Dobrushin received his Ph.D. at Moscow State University under the supervision of Andrey Kolmogorov.

Key takeaways

Roland Dobrushin belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Roland Dobrushin to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Roland Dobrushin from memory before moving on to harder problems.

Reference excerpt

Roland Lvovich Dobrushin (Russian: Рола́нд Льво́вич Добру́шин) (July 20, 1929 – November 12, 1995) was a mathematician who made important contributions to probability theory, mathematical physics, and information theory.

Life and work Dobrushin received his Ph.D. at Moscow State University under the supervision of Andrey Kolmogorov. In statistical mechanics, he introduced (simultaneously with Lanford and Ruelle) the DLR equations for the Gibbs measure. Together with Kotecký and Shlosman, he studied the formation of droplets in Ising-type models, providing mathematical justification of the Wulff construction. He was a foreign member of the American Academy of Arts and Sciences, Academia Europæa and US National Academy of Sciences. The Dobrushin prize was established in his honour.

Notes

References Ibragimov, I. A. (1997). "The work of R. L. Dobrushin on Markov processes". Russian Math. Surveys. 52 (2): 239–243. Bibcode:1997RuMaS..52..239I. doi:10.1070/rm1997v052n02abeh001767. MR 1480130. S2CID 250867778. Jaffe, A.; Lebowitz, J.; Sinai, Ya. (1997). "Roland L. Dobrushin". Comm. Math. Phys. 189 (2): 259–261. Bibcode:1997CMaPh.189..259J. doi:10.1007/s002200050199. MR 1480016. S2CID 121829879. Minlos, R. A. (1997). "R. L. Dobrushin—one of the founders of modern mathematical physics". Russian Math. Surveys. 52 (2): 251–256. Bibcode:1997RuMaS..52..251M. doi:10.1070/rm1997v052n02abeh001772. MR 1480132. S2CID 250856740. Prelov, V. V. (1997). "Information theory in the scientific work of R. L. Dobrushin". Russian Math. Surveys. 52 (2): 245–249. Bibcode:1997RuMaS..52..245P. doi:10.1070/rm1997v052n02abeh001771. MR 1480131. S2CID 250858169.

External links Roland Dobrushin at the Mathematics Genealogy Project Memorial website. Biography (in Russian) Obituary from The Independent

Illustrations

Worked examples

Example 1 — a first encounter with Roland Dobrushin

Start with the simplest possible case. Write down what Roland Dobrushin claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Roland Dobrushin before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Roland Dobrushin ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Roland Dobrushin

In research: Roland Dobrushin appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Roland Dobrushin in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Roland Dobrushin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1929 births, 1995 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Roland Dobrushin outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Roland Dobrushin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Roland Dobrushin means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Roland Dobrushin out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Roland Dobrushin in simple terms?

Why does Roland Dobrushin matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Roland Dobrushin?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Roland Dobrushin.