Related papers: Phase-Transition in Binary Sequences with Long-Ran…
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
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…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…
When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of…
It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…
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…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically…
Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic…
Let $(\{X_i(t)\}_{i\in \mathbb{Z}^d})_{t\geq 0}$ be the system of interacting diffusions on $[0,\infty)$ defined by the following collection of coupled stochastic differential equations: \begin{eqnarray}dX_i(t)=\sum\limits_{j\in…
In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here,…
This work addresses the superdiffusive motion of a discrete time random walker on ordered discrete substrates and complex networks with the presence of long-range interactions (LRIs). In ordered regular lattices, where LRIs have a clear…
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…
In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods. We furthermore employed the imaginary vector potential methods for calculating the localization lengths. Especially we…