相关论文: Random walk on disordered networks
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
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…
We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arc-length along the random walk as fictitous time, the resulting Langevin equation…
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version…