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The enormous increase of popularity and use of the worldwide web has led in the recent years to important changes in the ways people communicate. An interesting example of this fact is provided by the now very popular social annotation systems, through which users annotate resources (such as web pages or digital photographs) with keywords known as "tags."(More)
In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,. .. , N), which all start their random motion simultaneously at the same point in space. For each realization of the search process, we record the unordered set of time moments {τ k }, where τ(More)
Using path-integral techniques, we compute exactly the distribution of the maximal height Hp of p nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions p watermelons with a wall, and bridges p watermelons without a wall, for all integer p>or=1. For large p, we show that <Hp> approximately square root 2p(More)
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with κ = 4 whereas their fractal dimension is d s = 1.25, and therefore their behavior cannot be(More)
We investigate, analytically near the dimension d(uc) =4 and numerically in d=3 , the nonequilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the exact renormalization-group method to one loop, we compute the two times t, t(w) correlation function and fluctuation dissipation ratio (FDR) for any Fourier mode of the(More)
We study properties of a random walk in a generalized Sinai model, in which a quenched random potential is a trajectory of a fractional Brownian motion with arbitrary Hurst parameter H, 0<H<1, so that the random force field displays strong spatial correlations. In this case, the disorder-average mean-square displacement grows in proportion to log(2/H)(n), n(More)
We study the statistics of the number of records R(n,N) for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance(More)
We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e., below the critical temperature T(c), the disorder(More)
We study the nonequilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of ballistic annihilation therefore constantly loses particles. The dynamics of perturbations around the free decay regime is investigated using the(More)