Russell Lyons, Ron Peled, Oded Schramm
The number of spanning trees in the giant component of the random graph G(n, c/n) (c>1) grows like exp{m(f(c)+o(1))} as n →∞,wherem is the number of vertices in the giant component. The...
Stationary map coloring (2009)
Angel, Omer, Benjamini, Itai, Gurel-Gurevich, Ori, Meyerovitch, Tom, Peled, Ron
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 function of the...
Simple Universal Bounds for Chebyshev-Type Quadratures (2009)
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 bounds for the smallest possible n...
Phase Transitions in Gravitational Allocation (2009)
Chatterjee, Sourav, Peled, Ron, Peres, Yuval, Romik, Dan
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, we showed the...
On k-wise independent distributions and Boolean functions (2008)
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 identically...
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
The Maximal Probability that k-wise Independent Bits are All 1 (2007)
Peled, Ron, Yadin, Ariel, Yehudayoff, Amir
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 with identical...
Growth of the Number of Spanning Trees of the Erd\"os-R\'enyi Giant Component (2007)
Lyons, Russell, Peled, Ron, Schramm, Oded
The number of spanning trees in the giant component of the random graph $\G(n, c/n)$ ($c>1$) grows like $\exp\big\{m\big(f(c)+o(1)\big)\big\}$ as $n\to\infty$, where $m$ is the number of vertices in...
On rough isometries of Poisson processes on the line (2007)
Intuitively, two metric spaces are rough isometric (or quasi-isometric) if their metric structure is the same in the large scale, ignoring fine details. This concept has proved fundamental in the...
Gravitational allocation to Poisson points (2006)
Chatterjee, Sourav, Peled, Ron, Peres, Yuval, Romik, Dan
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 allocating to each of the...
Bhamidi, Shankar, Evans, Steven N., Peled, Ron, Ralph, Peter
Motivated by L\'{e}vy'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 that is unbounded...
Restoring Topology from Shifts (2004)
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 article we expand on...