Publications (65)
Hole probability for zeroes of Gaussian Taylor series with finite radii of convergence
Jeremiah Buckley, Alon Nishry, Ron Peled +1
We study a family of random Taylor series with radius of convergence almost surely and independent identically distributed complex Gaussia…
Gravitational allocation to Poisson points
Sourav Chatterjee, Ron Peled, Yuval Peres +1
For d>=3, we construct a non-randomized, fair and translation-equivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R^d, defined by alloca…
On the trace of random walks on random graphs
Alan Frieze, Michael Krivelevich, Peleg Michaeli +1
We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any there exists such that the trace of the simple rando…
Long-range order in discrete spin systems
Ron Peled, Yinon Spinka
We establish long-range order for discrete nearest-neighbor spin systems on satisfying a certain symmetry assumption, when the dimension is higher than an explic…
Minimal surfaces in random environment
Barbara Dembin, Dor Elboim, Daniel Hadas +1
A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary con…
Phase Transitions in Gravitational Allocation
Sourav Chatterjee, Ron Peled, Yuval Peres +1
Given a Poisson point process of unit masses (``stars'') in dimension d>=3, Newtonian gravity partitions space into domains of attraction (cells) of equal volume. In earlier work,…
Limit distributions for Euclidean random permutations
Dor Elboim, Ron Peled
We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length , density , dimension and jump density …
Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models
Michael Aizenman, Matan Harel, Ron Peled +1
For a family of integer-valued height functions defined over the faces of planar graphs, we establish a relation between the probability of connection by level sets and the spin-sp…
Double roots of random Littlewood polynomials
Ron Peled, Arnab Sen, Ofer Zeitouni
We consider random polynomials whose coefficients are independent and uniform on {-1,1}. We prove that the probability that such a polynomial of degree n has a double root is o(n^{…
A recursive construction of t-wise uniform permutations
Hilary Finucane, Ron Peled, Yariv Yaari
We present a recursive construction of a (2t + 1)-wise uniform set of permutations on 2n objects using a (2t + 1) - (2n, n, \cdot) combinatorial design, a t-wise uniform set of per…
Delocalization of uniform graph homomorphisms from to
Nishant Chandgotia, Ron Peled, Scott Sheffield +1
Graph homomorphisms from the lattice to are functions on whose gradients equal one in absolute value. These functions are the height func…
Longest increasing path within the critical strip
Partha Dey, Mathew Joseph, Ron Peled
A Poisson point process of unit intensity is placed in the square . An increasing path is a curve connecting with which is non-decreasing in each coordinat…
Quantitative disorder effects in low-dimensional spin systems
Paul Dario, Matan Harel, Ron Peled
The Imry-Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin…
A differential version of the Chebyshev-Markov-Stieltjes inequalities
Shoni Gilboa, Ron Peled
We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be…
On the site percolation threshold of circle packings and planar graphs
Ron Peled
A circle packing is a collection of disks with disjoint interiors in the plane. It naturally defines a graph by tangency. It is shown that there exists such that the followin…
Growth of the Number of Spanning Trees of the Erdös-Rényi Giant Component
Russell Lyons, Ron Peled, Oded Schramm
The number of spanning trees in the giant component of the random graph $\G(n, c/n)$ () grows like as , where is the num…
The Fröhlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition
Vital Kharash, Ron Peled
We present the Fröhlich-Spencer proof of the Berezinskii-Kosterlitz-Thouless transition. Our treatment includes the proof of delocalization for the integer-valued discrete Gaussia…
Liquid-vapor transition in a model of a continuum particle system with finite-range modified Kac pair potential
Qidong He, Ian Jauslin, Joel Lebowitz +1
We prove the existence of a phase transition in dimension in a continuum particle system interacting with a pair potential containing a modified attractive Kac potential of r…
Columnar order in random packings of squares on the square lattice
Daniel Hadas, Ron Peled
We study random packings of squares with centers on the square lattice , in which the probability of a packing is proportional to to the number of s…
Exponential decay of loop lengths in the loop model with large
Hugo Duminil-Copin, Ron Peled, Wojciech Samotij +1
The loop model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n…
Stationary map coloring
Omer Angel, Itai Benjamini, Ori Gurel-Gurevich +2
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant…
Concentration inequalities for log-concave distributions with applications to random surface fluctuations
Alexander Magazinov, Ron Peled
We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp--Lieb concentration inequality, and an ine…
Lengths of Monotone Subsequences in a Mallows Permutation
Nayantara Bhatnagar, Ron Peled
We study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the Mallows measure. Under this measure, the probability of a pe…
Non-constant ground configurations in the disordered ferromagnet
Michal Bassan, Shoni Gilboa, Ron Peled
The disordered ferromagnet is a disordered version of the ferromagnetic Ising model in which the coupling constants are non-negative quenched random. A ground configuration is an i…
Random-field random surfaces
Paul Dario, Matan Harel, Ron Peled
We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The r…
On the Cycle Structure of Mallows Permutations
Alexey Gladkich, Ron Peled
We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation is proporti…
Macroscopic loops in the loop model at Nienhuis' critical point
Hugo Duminil-Copin, Alexander Glazman, Ron Peled +1
The loop model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n…
On rough isometries of Poisson processes on the line
Ron Peled
Intuitively, two metric spaces are rough isometric (or quasi-isometric) if their large-scale metric structure is the same, ignoring fine details. This concept has proven fundamenta…
Coalescence of geodesics and the BKS midpoint problem in planar first-passage percolation
Barbara Dembin, Dor Elboim, Ron Peled
We consider first-passage percolation on with independent and identically distributed weights whose common distribution is absolutely continuous with a finite exponen…
On the influence of edges in first-passage percolation on
Barbara Dembin, Dor Elboim, Ron Peled
We study first-passage percolation on , , with independent weights whose common distribution is compactly supported in with a uniformly-positive d…
Lectures on the Spin and Loop Models
Ron Peled, Yinon Spinka
The classical spin model is a model on a -dimensional lattice in which a vector on the -dimensional sphere is assigned to every lattice site and the vectors at adj…
Lipschitz Functions on Expanders are Typically Flat
Ron Peled, Wojciech Samotij, Amir Yehudayoff
This work studies the typical behavior of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M-Li…
Rigidity of proper colorings of
Ron Peled, Yinon Spinka
A proper -coloring of a domain in is a function assigning one of colors to each vertex of the domain such that adjacent vertices are colored differently. Samp…
Rigidity of 3-colorings of the discrete torus
Ohad N. Feldheim, Ron Peled
We prove that a uniformly chosen proper -coloring of the -dimensional discrete torus has a very rigid structure when the dimension is sufficiently high. We show that with…
Odd cutsets and the hard-core model on Z^d
Ron Peled, Wojciech Samotij
We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, th…
High-Dimensional Lipschitz Functions are Typically Flat
Ron Peled
A homomorphism height function on the -dimensional torus is a function taking integer values on the vertices of the torus with consecutive integers assigned to…
Probabilistic existence of regular combinatorial structures
Greg Kuperberg, Shachar Lovett, Ron Peled
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence…
Simple Universal Bounds for Chebyshev-Type Quadratures
Ron Peled
A Chebyshev-type quadrature for a probability measure sigma is a distribution which is uniform on n points and has the same first k moments as sigma. We give an upper bound for the…
Separating signal from noise
Nir Lev, Ron Peled, Yuval Peres
Suppose that a sequence of numbers (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations,…
On the critical fugacity of the hard-core model on regular bipartite graphs
Daniel Hadas, Ron Peled
We establish long-range order for the hard-core model on a finite, regular bipartite graph above a threshold fugacity given in terms of expansion parameters of the graph. The resul…
Three lectures on random proper colorings of
Ron Peled, Yinon Spinka
A proper -coloring of a graph is an assignment of one of colors to each vertex of the graph so that adjacent vertices are colored differently. Sample uniformly among all pro…
A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model
Ron Peled, Yinon Spinka
We give a general condition for a discrete spin system with nearest-neighbor interactions on the lattice to exhibit long-range order. The condition is applicable to…
Random Walk with Long-Range Constraints
Ron Peled, Yinon Spinka
We consider a model of a random height function with long-range constraints on a discrete segment. This model was suggested by Benjamini, Yadin and Yehudayoff and is a generalizati…
Power-law decay of weights and recurrence of the two-dimensional VRJP
Gady Kozma, Ron Peled
The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker is biased towards returning to previously visited vertices with the bias dep…
Matrix regularizing effects of Gaussian perturbations
Michael Aizenman, Ron Peled, Jeffrey Schenker +2
The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for , where is the base matrix and is sampled from the GOE or the…
Probabilistic existence of rigid combinatorial structures
Greg Kuperberg, Shachar Lovett, Ron Peled
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of…
Random Dirichlet series arising from records
Ron Peled, Yuval Peres, Jim Pitman +1
We study the distributions of the random Dirichlet series with parameters defined by where is a sequence of independen…
On the transition between the disordered and antiferroelectric phases of the 6-vertex model
Alexander Glazman, Ron Peled
The symmetric six-vertex model with parameters is expected to exhibit different behavior in the regimes (antiferroelectric), (disordered) and $|…
What does a typical metric space look like?
Gady Kozma, Tom Meyerovitch, Ron Peled +1
The collection of all metric spaces on points whose diameter is at most can naturally be viewed as a compact convex subset of , k…
Exponential decay of correlations in the 2D random field Ising model
Michael Aizenman, Matan Harel, Ron Peled
An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement…
Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms
Omri Cohen-Alloro, Ron Peled
Motivated by questions on the delocalization of random surfaces, we prove that random surfaces satisfying a Lipschitz constraint rarely develop extremal gradients. Previous proofs…
Delocalization of two-dimensional random surfaces with hard-core constraints
Piotr MiÅoÅ, Ron Peled
We study the fluctuations of random surfaces on a two-dimensional discrete torus. The random surfaces we consider are defined via a nearest-neighbor pair potential which we require…
Dynamical Localization for Random Band Matrices up to
Giorgio Cipolloni, Ron Peled, Jeffrey Schenker +1
We prove that a large class of Gaussian random band matrices with band width exhibits dynamical Anderson localization at all energies when . The proo…
Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
Shankar Bhamidi, Steven N. Evans, Ron Peled +1
Motivated by Lévy's characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary closed subset of the line t…
A power-law upper bound on the correlations in the 2D random field Ising model
Michael Aizenman, Ron Peled
As first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all te…
Macroscopic loops in the loop O(n) model via the XOR trick
Nicholas Crawford, Alexander Glazman, Matan Harel +1
The loop model is a family of probability measures on collections of non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight and an edge-weight $…
Grounded Lipschitz functions on trees are typically flat
Ron Peled, Wojciech Samotij, Amir Yehudayoff
A grounded M-Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most along edges and attains the value zero on the leaves. We stu…
On K-wise Independent Distributions and Boolean Functions
Itai Benjamini, Ori Gurel-Gurevich, Ron Peled
We pursue a systematic study of the following problem. Let f:{0,1}^n -> {0,1} be a (usually monotone) Boolean function whose behaviour is well understood when the input bits are id…
Poisson Thickening
Ori Gurel-Gurevich, Ron Peled
Let X be a Poisson point process of intensity lambda on the real line. A thickening of it is a (deterministic) measurable function f such that the union of X and f(X) is a Poisson…
Minimal surfaces in strongly correlated random environments
Barbara Dembin, Dor Elboim, Ron Peled
A minimal surface in a random environment (MSRE) is a -dimensional surface in -dimensional space which minimizes the sum of its elastic energy and its environment potenti…
Chebyshev-type Quadratures for Doubling Weights
Shoni Gilboa, Ron Peled
A Chebyshev-type quadrature for a given weight function is a quadrature formula with equal weights. In this work we show that a method presented by Kane may be used to produce tigh…
The Maximal Probability that k-wise Independent Bits are All 1
Ron Peled, Ariel Yadin, Amir Yehudayoff
A k-wise independent distribution on n bits is a joint distribution of the bits such that each k of them are independent. In this paper we consider k-wise independent distributions…
On the Wegner orbital model
Jeffrey Schenker, Ron Peled, Mira Shamis +1
The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disorde…
Restoring Topology from Shifts
Ron Peled
It is known that the topology of a Polish group is uniquely determined by its Borel structure and group operations, but this does not give us a way to find the topology. In this ar…
Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model
Ron Peled, Dan Romik
The dense O(1) loop model is a statistical physics model with connections to the quantum XXZ spin chain, alternating sign matrices, the six-vertex model and critical bond percolati…