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We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is caught when a predator jumps to the site occupied by the prey. We analyze the efficacy of a lazy, minimal-effort evasion(More)
We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability L N (t) that the leftmost particle remains the leftmost as a function of time and (ii) the laggard problem, the probability R N (t) that the rightmost particle never becomes the leftmost. We(More)
We study a class of directed random graphs. In these graphs, the interval [0, x] is the vertex set, and from each y ∈ [0, x], directed links are drawn to points in the interval (y, x] which are chosen uniformly with density one. We analyze the length of the longest directed path starting from the origin. In the x → ∞ limit, we employ traveling wave(More)
A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A + A + A → A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic behavior for the concentration of clusters of mass m at time t, C m (t) ∼ m −1/2 (log(t)/t) 3/4 , for 1 ≪ m ≪ t/(More)
We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a new node attaches to the target with the highest degree. Depending on precise details of the attachment rule, the(More)
Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution(More)
How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules — transactions that involve a fixed amount or a fixed(More)
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