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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)

- C.Mejia-Monasterio, G. Oshanin, G. Schehr
- 2011

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)

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)

- Raja Paul, Grégory Schehr
- 2008

– We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability Pc(t) of the global magnetization is found to decay algebraically with an exponent θc that we compute analytically in a dimensional expansion in d = 4 − ǫ. Corrections to Markov process… (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)

- Heiko Rieger, Raja Paul, Jae-Dong Noh, Grégory Schehr
- 2007

Results of theoretical studies of spatially confined systems via Monte Carlo simulations are reported. Three experimentally relevant systems are considered: 1) Ad-and desorption phenomena in nanoporous materials like Vycor glass; 2) Dipolar molecules on a graphite surface that undergo an orientational transition; 3) Non-equilibrium dynamics in… (More)

The interplay between disorder, quantum fluctuations, and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale L* is identified above which the physics of frozen clusters dominates. Below L* a strong-disorder fixed point determines scaling… (More)

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