Related papers: Walks with jumps: a neurobiologically motivated cl…
Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant…
We present a method to map the evolution of photonic random walks that is compatible with nonclassical input light. Our approach leverages a newly developed flexible waveguide platform to tune the jumping rate between spatial modes,…
We show the existence of a trace process at infinity for random walks on hyperbolic groups of conformal dimension < 2 and relate it to the existence of a reflecting random walk. To do so, we employ the theory of Dirichlet forms which…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
For a symmetric random walk in $Z^2$ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erd\H{o}s-Taylor conjecture and obtain the…
We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
The expected hitting time of discrete quantum walks on a hypercube (HC) is numerically known to be exponentially shorter than that of their classical analogs in terms of the scaling with the HC dimension. Recent numerical analyses…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a…
The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
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,…
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…
In the brain, neural activity undergoes directed flows between states, thus breaking time-reversal symmetry. At the same time, animals also exhibit irreversible flows between behavioral states. Yet it remains unclear whether -- and how --…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate…