203 citations · 3.5k across the 97 of their papers we have counts for
71 papers · 1 filter
Statistical properties of sites visited by independent random walks
E. Ben-Naim, P. L. Krapivsky
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice a…
Monotonicity in the averaging process
E. Ben-Naim, P. L. Krapivsky
We investigate an averaging process that describes how interacting agents approach consensus through binary interactions. In each elementary step, two agents are selected at random…
Jamming and Tiling in Fragmentation of Rectangles
E. Ben-Naim, P. L. Krapivsky
We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where bo…
Jamming and Tiling in Aggregation of Rectangles
D. S. Ben-Naim, E. Ben-Naim, P. L. Krapivsky
We study a random aggregation process involving rectangular clusters. In each aggregation event, two rectangles are chosen at random and if they have a compatible side, either vert…
Extinction and Survival in Two-Species Annihilation
J. G. Amar, E. Ben-Naim, S. M. Davis +1
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite…
Kinetics of Aggregation with Choice
E. Ben-Naim, P. L. Krapivsky
We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice,…
Kinetics of Diffusion-Controlled Annihilation with Sparse Initial Conditions
E. Ben-Naim, P. L. Krapivsky
We study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, bo…
Escape and Finite-Size Scaling in Diffusion-Controlled Annihilation
E. Ben-Naim, P. L. Krapivsky
We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and whe…
Scaling Exponents for Ordered Maxima
E. Ben-Naim, P. L. Krapivsky, N. W. Lemons
We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum…
Irreversible Reactions and Diffusive Escape: Stationary Properties
P. L. Krapivsky, E. Ben-Naim
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous in…
Fragmentation of Random Trees
Z. Kalay, E. Ben-Naim
We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nod…
Slow Kinetics of Brownian Maxima
E. Ben-Naim, P. L. Krapivsky
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing in…
Persistence of Random Walk Records
E. Ben-Naim, P. L. Krapivsky
We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. W…
First Passage in Conical Geometry and Ordering of Brownian Particles
E. Ben-Naim, P. L. Krapivsky
We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss…
Statistics of Superior Records
E. Ben-Naim, P. L. Krapivsky
We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running re…
Discrete Analog of the Burgers Equation
E. Ben-Naim, P. L. Krapivsky
We propose the set of coupled ordinary differential equations dn_j/dt=(n_{j-1})^2-(n_j)^2 as a discrete analog of the classic Burgers equation. We focus on traveling waves and tria…
Popularity-Driven Networking
E. Ben-Naim, P. L. Krapivsky
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the con…
Dynamics of Random Graphs with Bounded Degrees
E. Ben-Naim, P. L. Krapivsky
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller tha…
Kinetics of Ring Formation
E. Ben-Naim, P. L. Krapivsky
We study reversible polymerization of rings. In this stochastic process, two monomers bond and as a consequence, two disjoint rings may merge into a compound ring, or, a single rin…
On the Mixing of Diffusing Particles
E. Ben-Naim
We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pai…
First-Passage Exponents of Multiple Random Walks
E. Ben-Naim, P. L. Krapivsky
We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive…
Kinetics of First Passage in a Cone
E. Ben-Naim, P. L. Krapivsky
We study statistics of first passage inside a cone in arbitrary spatial dimension. The probability that a diffusing particle avoids the cone boundary decays algebraically with time…
First Passage Properties of the Polya Urn Process
Tibor Antal, E. Ben-Naim, P. L. Krapivsky
We study first passage statistics of the Polya urn model. In this random process, the urn contains two types of balls. In each step, one ball is drawn randomly from the urn, and su…
Random Ancestor Trees
E. Ben-Naim, P. L. Krapivsky
We investigate a network growth model in which the genealogy controls the evolution. In this model, a new node selects a random target node and links either to this target node, or…