mathematics

Ofer Zeitouni

Ofer Zeitouni 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 Ofer Zeitouni rather than just read about it. In short: Ofer Zeitouni (Hebrew: עפר זיתוני; born 23 October 1960, Haifa) is an Israeli mathematician, specializing in probability theory. Biography Zeitouni received his bachelor's degree in electrical engineering in 1980 from the Technion.

Key takeaways

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

Reference excerpt

Ofer Zeitouni (Hebrew: עפר זיתוני; born 23 October 1960, Haifa) is an Israeli mathematician, specializing in probability theory.

Biography Zeitouni received his bachelor's degree in electrical engineering in 1980 from the Technion. He obtained in 1986 his doctorate in electrical engineering under the supervision of Moshe Zakai with the thesis Bounds on the Conditional Density and Maximum a posteriori Estimators for the Nonlinear Filtering Problem. As a postdoc he was a visiting assistant professor at Brown University and at the Laboratory for Information and Decision Systems at MIT. He joined the Technion in 1989 as senior lecturer, and was promoted in 1991 to associate professor, and in 1997 to full professor in the department of electrical engineering. He is now a professor of Mathematics at the Weizmann Institute and at the Courant Institute, and was from 2002 to 2013 a part-time professor at the University of Minnesota. His research deals with stochastic processes and filtering theory with applications to control theory (electrical engineering), the spectral theory of random matrices, the theory of large deviations in probability theory, motion in random media, and extremes of logarithmically correlated fields. He was Invited Speaker with the talk Random Walks in Random Environments at the ICM in Beijing in 2002. Zeitouni is a Fellow of the American Mathematical Society, member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the Israel Academy of Sciences and Humanities. He is married and has two children.

Selected publications

Articles with Ildar Abdulovich Ibragimov: Ibragimov, Ildar; Zeitouni, Ofer (1997). "On roots of random polynomials". Trans. Amer. Math. Soc. 349 (6): 2427–2441. doi:10.1090/S0002-9947-97-01766-2. with Amir Dembo, Yuval Peres, and Jay Rosen: Dembo, Amir; Peres, Yuval; Rosen, Jay; Zeitouni, Ofer (2001). "Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk". Acta Mathematica. 186 (2): 239–270. doi:10.1007/BF02401841. with Amir Dembo, Bjorn Poonen, and Qi-Man Shao: Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer (2002). "Random polynomials having few or no real zeros". J. Amer. Math. Soc. 15 (4): 857–892. arXiv:math/0006113. doi:10.1090/S0894-0347-02-00386-7. with Amir Dembo, Yuval Peres, and Jay Rosen: Dembo, Amir; Peres, Yuval; Rosen, Jay; Zeitouni, Ofer (2002). "Thick points for intersections of planar sample paths". Trans. Amer. Math. Soc. 354 (12): 4969–5003. doi:10.1090/S0002-9947-02-03080-5. Zeitouni, Ofer (2004). "Part II: Random walks in random environment". In: Lectures on probability theory and statistics. Lecture Notes in Mathematics. Vol. 1837. Berlin, Heidelberg: Springer. pp. 190–312. doi:10.1007/978-3-540-39874-5_2. ISBN 978-3-540-20832-7.

Books with Greg W. Anderson and Alice Guionnet: Introduction to Random Matrices, Cambridge University Press 2010 with Amir Dembo: Large Deviations Techniques and Applications, Springer 1998, Dembo, Amir; Zeitouni, Ofer (2009). 2nd edition, corrected printing of 1998 edition. Springer. ISBN 9783642033117; pbk{{cite book}}: CS1 maint: postscript (link)

Sources Zhan Shi: Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien, d’après Dembo, Peres, Rosen, Zeitouni, Seminaire Bourbaki, No. 951, 2005

References

External links Ofer Zeitouni's home page, Weizmann Institute Ofer Zeitouni, What happens when a person strolling along an intersecting path chooses directions with a roll of the dice?, Weizmann Institute

Illustrations

Worked examples

Example 1 — a first encounter with Ofer Zeitouni

Start with the simplest possible case. Write down what Ofer Zeitouni 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 Ofer Zeitouni 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 Ofer Zeitouni 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 Ofer Zeitouni

In research: Ofer Zeitouni 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 Ofer Zeitouni 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: Ofer Zeitouni is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1960 births, Academic staff of Technion – Israel Institute of Technology, Academic staff of Weizmann Institute of Science, so understanding it makes those chapters shorter.
In everyday life: Look for Ofer Zeitouni 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 Ofer Zeitouni in 20 minutes

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

Frequently asked questions

What is Ofer Zeitouni in simple terms?

Ofer Zeitouni (Hebrew: עפר זיתוני; born 23 October 1960, Haifa) is an Israeli mathematician, specializing in probability theory. Biography Zeitouni received his bachelor's degree in electrical engineering in 1980 from the Technion.

Why does Ofer Zeitouni 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 Ofer Zeitouni?

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 Ofer Zeitouni.