Ronen Eldan's home page - דף הבית של רונן אלדן

	Ronen Eldan's home page דף הבית של רונן אלדן
	*I'm faculty in the Department of Mathematics at the Weizmann Institute of Science.*
	*(Currently, I'm on Sabbatical at the Institute for Advanced Study, Princeton)*




	E-mail :My first name followed by my last (no dashes and such) at gmail.com

	Address: Department of Mathematics, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

I manufacture latex and latex-related products.

My interests, on a low resolution: Anything that's high-dimensional, whether it's Probability, Functional Analysis, Metric Geometry, Computational Geometry, Mathematical Physics or Learning Theory.

My interests, on a higher resolution: Functional inequalities, Concentration of measure, High-dimensional convex geometry, Stochastic calculus, High-dimensional probabilistic algorithms, Probabilistic structures (with a geometric nature), Gaussian fields, Central limit theorems, Interacting particle systems, Random Graphs, Boolean analysis, Convex optimization, Neural networks, Computational Complexity.

One of my main long-term projects is to develop a technique, based on pathwise analysis and stochastic calculus, for analyzing high-dimensional objects. This note gives a flavor of the technique and some of its applications (it will appear in the 2022 ICM Proceedings).

In the unlikely scenario that someone wants to know what my interests are in a yet higher resolution, here is a link to a (more or less) updated research statement.

(as you can probably guess from the look of this page, I am also an avant-garde web designer).

Some past teaching

Geometry and Data Science (course page)
Random walks and Algorithms

Lecture notes for the talk series: From stochastic calculus to geometric inequalities (Concentration week on Geometric Functional Analysis)

Students

Dan Mikulincer (Ph.D., 2021. Now at MIT)

Renan Gross (Ph.D., ongoing) (you should check out Renan's blog!)

Arianna Piana (Ph.D., ongoing).

Yotam Alexander (M.Sc., 2018).

Omer Shamir (M.Sc., 2020).

Tali Goldman (M.Sc., ongoing).

Publications and Preprints

For a full list of publications, see the Arxiv, Google Scholar or Mathscinet.

Some (randomly) selected papers:

R. Eldan, A Polynomial Number of Random Points does not Determine the Volume of a Convex Body. Discrete Comput. Geom. 46 (2011), no. 1, 29–47.
R. Eldan, Thin shell implies spectral gap via a stochastic localization scheme. Geom. Funct. Anal. April 2013, Volume 23, Issue 2, pp 532-569 (2013).
R. Eldan, A two-sided estimate for the Gaussian noise stability deficit. Invent. Math. 201 (2015), no. 2, 561–624.
S. Bubeck and R. Eldan Multi-scale exploration of convex functions and bandit convex optimization. Math. Stat. Learn. 1 (2018), no. 1, 73–100. (COLT 2016, Best paper award).
S. Bubeck, R. Eldan and YT. Lee Kernel-based methods for bandit convex optimization J. ACM 68 (2021), no. 4, Art. 25, 37 pp.
R. Eldan and J.R. Lee, Regularization under diffusion and anticoncentration of the information content. Duke math. J. 167 (2018), no. 5, 969–993. .
R. Eldan and B. Klartag, Approximately Gaussian marginals and the hyperplane conjecture. Concentration, functional inequalities and isoperimetry, 55–68, Contemp. Math., 545, Amer. Math. Soc.
R. Eldan, Diffusion limited aggregation in the hyperbolic plane. Ann. Probab. Volume 43, Number 4 (2015), 2084-2118.
J. Ding, R. Eldan and A. Zhai, On Multiple Peaks and Large Deviations of Gaussian Processes., Ann. Probab. Vol. 43, No. 4, 2084–2118, 2015.
R. Eldan Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations. Geom. Funct. Anal. 28 (2018), no. 6, 1548–1596.
R. Eldan and O. Shamir The Power of Depth for Feedforward Neural Networks, Conference on Learning Theory (COLT) 2016.
R. Eldan, D. Mikulincer and A. Zhai, The CLT in high dimensions: quantitative bounds via martingale embedding. Ann. Probab. 48 (2020), no. 5, 2494–2524.
R. Eldan, Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation. Probab. Theory Related Fields 176 (2020), no. 3-4, 737–755.
R. Eldan and D. Mikulincer, Stability of the Shannon-Stam inequality via the Follmer process. Probab. Theory Related Fields 177 (2020), no. 3-4, 891–922.
R. Eldan and R. Gross Concentration on the Boolean hypercube via pathwise stochastic analysis. Invent. Math. (to appear).
Y. Chen and R. Eldan Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains. preprint (2022).
R. Eldan Analysis of high-dimensional distributions using pathwise methods. to appear in the 2022 ICM Proceedings.

Some of my favorite publications, by other authors: *1* *2* *3* *4* *5* *6* *7* *8*