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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)

- Dong Wang, Mark Newman, Sasha Sodin, Ioana Dumitriu, Ivan Corwin, Alexei Borodin +3 others
- 2013

How long does it take to compute the eigenvalues of a random symmetric matrix?

- K Schwarz, A Karrenbauer, G Schehr, H Rieger
- 2009

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)

A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a nonequilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation mechanism in these systems. We show that as time progresses an inner core region around the resetting point reaches the… (More)

We consider the excursions, i.e., the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{max}(t) up to time t. For smooth processes, we find a universal linear growth l_{max}(t) approximately Q_{infinity}t with a model dependent amplitude… (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)

We study the aging properties, in particular the two-time autocorrelations, of the two-dimensional randomly diluted Ising ferromagnet below the critical temperature via Monte Carlo simulations. We find that the autocorrelation function displays additive aging C(t,t{w})=C{st}(t)+C{ag}(t,t{w}), where the stationary part Cst} decays algebraically. The aging… (More)