Related papers: Slow relaxation dynamics and aging in random walks…
We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy…
We review the aging phenomenon in the context of the simplest trap model, Bouchaud's REM-like trap model, from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalized exactly. Using…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
Here we consider the topological properties of the integrated networks emerging from the activity driven model [Perra at al. Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution…
We review the ageing phenomenon in the context of simplest trap model, Bouchaud's REM-like trap model from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalised exactly. Using this…
We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical…
In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchaud's 'REM-like' trap model. We show that, below the critical temperature, if we consider a…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
We model financial transactions as random walks on activity-driven temporal networks. By enforcing fund conservation, our framework analytically derives heavy-tailed distributions for the stationary balances and transaction sizes.…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…