Annecy, April 2012.

Ron Peled's Home Page

I am a full professor in the School of Mathematical Sciences of Tel Aviv University. My research interests are in Probability Theory, Statistical Physics and related fields.

Starting in the summer of 2024, I am a full professor at the Department of Mathematics of the University of Maryland, on leave from Tel Aviv University.

In the 2022-2024 academic years I visited Princeton University and the Institute for Advanced Study.

Address:
231 Schreiber Building, School of Mathematical Sciences, Tel Aviv University
Ramat Aviv, Tel Aviv 69978, Israel

Email: peledron (* the at symbol *) tauex.tau.ac.il
Phone: (+972)3-6408034

Papers

Minimal surfaces in random environment. Joint with Barbara Dembin, Dor Elboim and Daniel Hadas. Preprint.
Non-constant ground configurations in the disordered ferromagnet. Joint with Michal Bassan and Shoni Gilboa. Preprint.
On the influence of edges in first-passage percolation on Z^d. Joint with Barbara Dembin and Dor Elboim. To appear in Annals of Probability.
Dynamical Localization for Random Band Matrices up to W<<N^1/4. Joint with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro. Communications in Mathematical Physics 405, no. 3 (2024): 82.
Columnar order in random packings of 2×2 squares on the square lattice. Joint with Daniel Hadas. Preprint.
Coalescence of geodesics and the BKS midpoint problem in planar first-passage percolation. Joint with Barbara Dembin and Dor Elboim. Geometric and Functional Analysis (2024): 1-65.
Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models. Joint with Michael Aizenman, Matan Harel and Jacob Shapiro. Preprint.
What does a typical metric space look like?. Joint with Gady Kozma, Tom Meyerovitch and Wojciech Samotij. Annales de l’Institut Henri Poincaré (B) Probabilités et statistiques, vol. 60, no. 1, pp. 11-53, 2024, special issue dedicated to Dima Ioffe.
Random-field random surfaces. Joint with Paul Dario and Matan Harel. Probability Theory and Related Fields 186, no. 1-2 (2023): 91-158.
Quantitative disorder effects in low-dimensional spin systems. Joint with Paul Dario and Matan Harel. To appear in Communications in Mathematical Physics.
Long-range order in discrete spin systems. Joint with Yinon Spinka. Preprint.
Concentration inequalities for log-concave distributions with applications to random surface fluctuations. Joint with Alexander Magazinov. Annals of Probability 50(2): 735-770 (2022).
Macroscopic loops in the loop O(n) model via the XOR trick. Joint with Nicholas Crawford, Alexander Glazman and Matan Harel. To appear in Annals of Probability.
Three lectures on random proper colorings of Z^d. Joint with Yinon Spinka. Preprint.
On the site percolation threshold of circle packings and planar graphs. Preprint.
Power-law decay of weights and recurrence of the two-dimensional VRJP. Joint with Gady Kozma. Electronic Journal of Probability 26: 1-19 (2021).
On the transition between the disordered and antiferroelectric phases of the 6-vertex model. Joint with Alexander Glazman. Electronic Journal of Probability 28 (2023): 1-53.
Exponential decay of correlations in the 2D random field Ising model. Joint with Michael Aizenman and Matan Harel. Journal of Statistical Physics 180, 304–331 (2020), special issue celebrating Joel Lebowitz.
Delocalization of uniform graph homomorphisms from Z² to Z. Joint with Nishant Chandgotia, Scott Sheffield and Martin Tassy. Communications in Mathematical Physics 387, 621–647 (2021).
Longest increasing path within the critical strip. Joint with Partha Dey and Mathew Joseph. Israel Journal of Mathematics (2023): 1-41.
A power-law upper bound on the correlations in the 2D random field Ising model. Joint with Michael Aizenman. Communications in Mathematical Physics 372, 865–892 (2019).
Rigidity of proper colorings of Z^d. Joint with Yinon Spinka. Inventiones Mathematicae 232, no. 1 (2023): 79-162.
Appendix in On locally repeated values of arithmetic functions over F_q[T] by Ze'ev Rudnick. The Quarterly Journal of Mathematics (2018).
A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model. Joint with Yinon Spinka. Preprint.
Limit distributions for Euclidean random permutations. Joint with Dor Elboim. Communications in Mathematical Physics 369, 457–522 (2019).
The Fröhlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition. Joint with Vital Kharash. Preprint.
Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms. Joint with Omri Cohen-Alloro. Annals of Applied Probability 30 (5) 2439 - 2464, 2020.
Lectures on the spin and loop O(n) models. Joint with Yinon Spinka. Sojourns in Probability Theory and Statistical Physics - I, celebrating Charles Newman's 70th birthday.
Macroscopic loops in the loop O(n) model at Nienhuis' critical point. Joint with Hugo Duminil-Copin, Alexander Glazman and Yinon Spinka. Journal of the European Mathematical Society 23 (2021), 315-347.
On the Wegner orbital model. Joint with Jeffrey Schenker, Mira Shamis and Sasha Sodin. International Mathematics Research Notices 2019(4), pp.1030-1058.
Hole probability for zeroes of Gaussian Taylor series with finite radii of convergence. Joint with Jeremiah Buckley, Alon Nishry and Mikhail Sodin. Probability Theory and Related Fields 171, no. 1-2 (2018): 377-430.
On the Cycle Structure of Mallows Permutations. Joint with Alexey Gladkich. Annals of Probability 46 (2018), no. 2, 1114-1169.
Matrix regularizing effects of Gaussian perturbations. Joint with Michael Aizenman, Jeffrey Schenker, Mira Shamis and Sasha Sodin. Communications in Contemporary Mathematics 19 (2017), no. 3, 1750028, 22pp.
On the trace of random walks on random graphs. Joint with Alan Frieze, Michael Krivelevich and Peleg Michaeli. Proceedings of the London Mathematical Society 116 (2018), no. 4, 847-877.
Chebyshev-type Quadratures for Doubling Weights. Joint with Shoni Gilboa. Constructive Approximation 45 (2017), no. 2, 193-216.
Random Dirichlet series arising from records. Joint with Yuval Peres, Jim Pitman and Ryokichi Tanaka. Journal of the Mathematical Society of Japan 67.4 (2015): 1705-1723.
Exponential decay of loop lengths in the loop O(n) model with large n. Joint with Hugo Duminil-Copin, Wojciech Samotij and Yinon Spinka. Communications in Mathematical Physics 349 (2017), no. 3, 777-817.
Double roots of random Littlewood polynomials. Joint with Arnab Sen and Ofer Zeitouni. Israel Journal of Mathematics 213.1 (2016): 55-77.
Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model. Joint with Dan Romik. Séminaire Lotharingien de Combinatoire 73 (2015): B73b.
A differential version of the Chebyshev-Markov-Stieltjes inequalities. Joint with Shoni Gilboa. Journal of Approximation Theory 196 (2015), 13-54.
Delocalization of two-dimensional random surfaces with hard-core constraints. Joint with Piotr Miłoś. Communications in Mathematical Physics 340.1 (2015): 1-46.
Separating signal from noise. Joint with Nir Lev and Yuval Peres. Proceedings of the London Mathematical Society 110 (2015), no. 4, 883-931.
Random Walk with Long-Range Constraints. Joint with Yinon Spinka. Electronic Journal of Probability 19 (2014), no. 52, 1-54.
Rigidity of 3-colorings of the discrete torus. Joint with Ohad N. Feldheim. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, vol. 54, no. 2, pp. 952-994. Institut Henri Poincaré, 2018.
Lengths of Monotone Subsequences in a Mallows Permutation. Joint with Nayantara Bhatnagar. Probability Theory and Related Fields 161 (2015), no. 3-4, 719-780.
Grounded Lipschitz functions on trees are typically flat. Joint with Wojciech Samotij and Amir Yehudayoff. Electronic Communications in Probability 18 (2013), no. 55, 1-9.
Probabilistic existence of regular combinatorial structures. Joint with Greg Kuperberg and Shachar Lovett. Geometric And Functional Analysis 27 (2017), no. 4, 919-972. Extended abstract version appeared in STOC 2012.
Lipschitz Functions on Expanders are Typically Flat. Joint with Wojciech Samotij and Amir Yehudayoff. Combinatorics, Probability and Computing 22 (2013), no. 4, 566-591.
A recursive construction of t-wise uniform permutations. Joint with Hilary Finucane and Yariv Yaari. Random Structures and Algorithms 46 (2015), no. 3, 531–540.
Odd Cutsets and the Hard-core Model on Z^d. Joint with Wojciech Samotij. Annales de l'Institut Henri Poincaré Probabilités et Statistiques 50 (2014), no. 3, 975-998.
High-Dimensional Lipschitz Functions are Typically Flat. Annals of Probability 45 (2017), no. 3, 1351--1447.
Poisson Thickening. Joint with Ori Gurel-Gurevich. Israel Journal of Mathematics 196 (2013), 215-234.
Stationary Map Coloring. Joint with Omer Angel, Itai Benjamini, Ori Gurel-Gurevich, Tom Meyerovitch. Annales de l'Institut Henri Poincaré 48, No. 2 (2012), 327-342.
Gravitational Allocation to Poisson Points. Joint with Sourav Chatterjee, Yuval Peres and Dan Romik. Annals of Mathematics 172 (2010), no. 1, 617--671.
Phase Transitions in Gravitational Allocation. Joint with Sourav Chatterjee, Yuval Peres and Dan Romik. Geometric And Functional Analysis 20 (2010), No. 4, 870-917.
Simple Universal Bounds for Chebyshev-Type Quadratures. Journal of Approximation Theory 162 (2010), No. 12, 2317-2348.
The Maximal Probability that k-wise Independent Bits are All 1. Joint with Ariel Yadin and Amir Yehudayoff. Random Structures & Algorithms 38 (2011), No. 4, 502-525.
Growth of the Number of Spanning Trees of the Erdös-Rényi Giant Component. Joint with Russell Lyons and Oded Schramm. Combinatorics, Probability & Computing 17(5): 711-726 (2008).
On Rough Isometries of Poisson Processes on the Line. Annals of Applied Probability, Volume 20, Number 2 (2010), 462-494.
Brownian Motion on Time Scales, basic hypergeometric functions, and some continued fractions of Ramanujan. Joint with Shankar Bhamidi, Steve Evans and Peter Ralph. Probability and statistics: essays in honor of David A. Freedman, 42-75, Inst. Math. Stat. Collect., 2, Inst. Math. Statist., Beachwood, OH, 2008.
On k-wise Independent Events and Percolation. Joint with Itai Benjamini and Ori-Gurel Gurevich. Extended abstract version and slideshow are available.
Restoring Topology from Shifts. My master's thesis under Prof. Boris Tsirelson. Preprint.

Support from the Israel Science Foundation grants 1048/11, 861/15, 1971/19 and 2340/23, the Marie Skłodowska-Curie Actions International Reintegration Grant SPTRF, the ERC Starting Grant LocalOrder and the ERC Consolidator Grant Transitions is gratefully acknowledged.

Uniformly sampled homomorphism and Lipschitz functions in 2 and 3 dimensions Left column: homomorphism and Lipschitz functions on a 100 x 100 square with zero boundary values Right column: middle slice of homomorphism and Lipschitz functions on a 100 x 100 x 100 cube with zero boundary values	Top: the outermost level sets separating zeros and ones of a uniformly sampled homomorphism on a 40 x 40 and 300 x 300 squares with zero boundary values (pictures produced with the help of Steven M. Heilman) Bottom: The shift transformation applied to the level set of a homomorphism function. This transformation is a major tool in the analysis of homomorphism functions in high dimensions
Gradient Flow / Gravitational Allocation (pictures based on code by Manjunath Krishnapur) First row: Allocation to the zeros of the planar, hyperbolic and spherical canonical Gaussian Analytic Functions (all cells have equal areas!) Second row: The potential for the allocations to the planar and hyperbolic Gaussian Analytic Functions.
K-wise independent percolation	4 coloring of Poisson-Voronoi map.
Rough isometry of 1D percolations	Brownian motion on a geometric state space and on the Cantor set (pictures courtesy of Peter Ralph)

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