Related papers: Understanding random-walk dynamical phase coexiste…
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…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
Quantum processes of inherent dynamical nature, such as quantum walks (QWs), defy a description in terms of an equilibrium statistical physics ensemble. Up to now, it has remained a key challenge to identify general principles behind the…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
We study an integrable spin chain with three spin interactions and the staggered field ($\lambda$) while the latter is quenched either slowly (in a linear fashion in time ($t$) as $t/\tau$ where $t$ goes from a large negative value to a…
We report on the discovery of a quantum tri-critical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system.…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional…
Dynamical quantum phase transitions (DQPTs) are a class of non-equilibrium phase transitions that occur in many-body quantum systems during real-time evolution, rather than through parameter tuning as in conventional phase transitions. This…
We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit…
The interaction between individuals in biological populations, dilute components of chemical systems, or particles transported by turbulent flows depends critically on their contact statistics. This work clarifies those statistics under the…
A random walk is performed over a disordered media composed of $N$ sites random and uniformly distributed inside a $d$-dimensional hypercube. The walker cannot remain in the same site and hops to one of its $n$ neighboring sites with a…
Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
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…
Motivated by a connection to the infinite Ginibre point process, decoupled random walks were introduced in a recent article Alsmeyer, Iksanov and Kabluchko (2025). The decoupled random walk is a sequence of independent random variables, in…
We study dynamical quantum phase transitions (DQPTs) in the extended Bose-Hubbard model after a sudden quench of the nearest-neighbor interaction strength. Using the time-dependent density matrix renormalization group, we demonstrate that…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…