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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)
We study the probability density function P(h(m), L) of the maximum relative height h(m) in a wide class of one-dimensional solid-on-solid models of finite size L. For all these lattice models, in the large-L limit, a central limit argument shows that, for periodic boundary conditions, P(h(m), L) takes a universal scaling form P(h(m), L) approximately(More)
We study the distribution function P(ω) of the random variable ω=τ(1)/(τ(1)+···+τ(N)), where τ(k)'s are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τ(k)'s are independent and identically distributed random variables with a distribution Ψ(τ) characterized by(More)
We investigate the statistics of the gap G(n) between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration L(n) which separates the occurrence of these two extremal positions. The distribution of the jumps η(i)'s of the RW, f(η), is symmetric and its Fourier transform has the small k behavior(More)
We study the extreme statistics of N nonintersecting Brownian motions (vicious walkers) over a unit time interval in one dimension. Using path-integral techniques we compute exactly the joint distribution of the maximum M and of the time τ(M) at which this maximum is reached. We focus in particular on nonintersecting Brownian bridges ("watermelons without(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 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)