Related papers: Euler Walk on a Cayley Tree
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias $\rho \in (0,\infty)$ towards the root, and exhibit a phase transition for…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
We study the asymptotic behavior of ``true" self-avoiding random walks on general infinite locally finite trees. In this model, the walk starts at the root and, at each step, from its current vertex chooses a neighboring edge to traverse…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study a $U(1)\times U(1)$ system with short-range interactions and mutual $\theta=2\pi/3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem, and perform a Monte Carlo study. We find a…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
We introduce a two-dimensional walk model in which a random walker can only move on the first quarter of a two-dimensional plane. We calculate the partition function of this walk model using a transfer matrix method and show that the model…
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
Tracking the movement of tracer particles has long been a strategy for uncovering complex structures. Here, we study discrete-time random walks on finite Cayley trees to infer key parameters such as tree depth and geometric bias toward the…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by…
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
There are rich emergent phase behaviors in non-equilibrium active systems. Flocking and clustering are two representative dynamic phases. The relationship between these two phases is still unclear. In the paper, we numerically investigate…
Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, $E \propto t^{\eta}$ with $\eta=0.46(2)$, and compressed-exponential momentum…