mathematics

Michael Aizenman

Michael Aizenman 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 Michael Aizenman rather than just read about it. In short: Michael Aizenman (Hebrew: מיכאל אייזנמן; born 28 August 1945) is an American-Israeli mathematician and a physicist at Princeton University, working in the fields of mathematical physics, statistical mechanics, functional analysis and probability theory. The highlights of his work include: the triviality of a class of scalar quantum field theories in more than three dimensions; a description of the phase transition i…

Key takeaways

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

Reference excerpt

Michael Aizenman (Hebrew: מיכאל אייזנמן; born 28 August 1945) is an American-Israeli mathematician and a physicist at Princeton University, working in the fields of mathematical physics, statistical mechanics, functional analysis and probability theory. The highlights of his work include: the triviality of a class of scalar quantum field theories in more than three dimensions; a description of the phase transition in the Ising model in three and more dimensions; the sharpness of the phase transition in percolation theory; a method for the study of spectral and dynamical localization for random Schrödinger operators; and insights concerning conformal invariance in two-dimensional percolation.

Biography Aizenman is a Jewish American - Israeli who was born in Russia. He was an undergraduate at the Hebrew University of Jerusalem. He was awarded his PhD in 1975 at Yeshiva University (Belfer Graduate School of Science), New York City, with advisor Joel Lebowitz. After postdoctoral appointments at the Courant Institute of Mathematical Sciences of New York University (1974–75), and Princeton University (1975–1977), with Elliott H. Lieb, he was appointed assistant professor at Princeton. In 1982 he moved to Rutgers University as associate professor and then full professor. In 1987 he moved to the Courant Institute and in 1990 returned to Princeton as professor of mathematics and physics. He was several times a visiting scholar at the Institute for Advanced Study, in 1984–85, 1991–92, and 1997–98, and is a regular visiting scholar at the Weizmann Institute of Science.

Honors and awards Norbert Wiener Prize (1990) of the Amer. Math. Soc. and SIAM for "his outstanding contribution of original and non-perturbative mathematical methods in statistical mechanics by means of which he was able to solve several long open important problems concerning critical phenomena, phase transitions, and quantum field theory." Brouwer Medal (2002) of the Dutch Math. Soc. and the Royal Dutch Academy of Arts and Sciences Dannie Heineman Prize in Mathematical Physics (2010), of APS and AIP Henri Poincaré Prize (2018) of IAMP. Aizenman received honorary degrees (DHC) from Université de Cergy-Pontoise (2009) and Technion (2018), and is a member of National Academy of Sciences (1997), American Academy of Arts and Sciences (2017), and Academia Europaea (2016). During 2001-2012 he served as the editor-in-chief of Communications in Mathematical Physics.

Publications Random Operators: Disorder Effects on Quantum Spectra and Dynamics, by M. Aizenman and S. Warzel (AMS 2015). Aizenman, Michael; Duminil-Copin, Hugo (2021), Marginal triviality of the scaling limits of critical 4D Ising and ϕ44 models. Ann. of Math. (2) 194 (2021), no. 1, 163–235.

References

External links Princeton home page Michael Aizenman at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Michael Aizenman

Start with the simplest possible case. Write down what Michael Aizenman 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 Michael Aizenman 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 Michael Aizenman 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 Michael Aizenman

In research: Michael Aizenman 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 Michael Aizenman 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: Michael Aizenman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Aizenman 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Michael Aizenman in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Michael Aizenman 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 Michael Aizenman out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Michael Aizenman in simple terms?

Why does Michael Aizenman 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 Michael Aizenman?

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 Michael Aizenman.