Joël De Coninck, François Dunlop, Thierry Huillet Abstract: We consider random walks Xn in Z+, obeying a detailed balance condition, with a weak drift towards the origin when Xn ր ∞. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are discussed in terms of recurrence versus wetting. A ...

Quantum walks (QWs) exhibit different properties compared with classical random (RWs), most notably by linear spreading and localization. In the meantime, that replicate quantum walks, which we refer to as quantum-walk-replicating (QWRWs), have been studied in literature where eventual of QWRW coincide those QWs. However, consider unique attributes QWRWs not fully utilized former studies obtain...

How can we augment a dynamic graph for improving the performance of neural networks? Graph augmentation has been widely utilized to boost learning GNN-based models. However, most existing approaches only enhance spatial structure within an input static by transforming graph, and do not consider dynamics caused time such as temporal locality, i.e., recent edges are more influential than earlier ...

We present an exact method for speeding up random walk in two-dimensional complicated lattice environments. To this end, we derive the discrete two-dimensional probability distribution function for a diffusing particle starting at the center of a square of linear size s. This is used to propagate random walkers from the center of the square to sites which are nearest neighbors to its perimeter ...

We consider discrete non-divergence form difference operators in a random environment and the corresponding process – walk balanced Zd with finite range of dependence. first quantify ergodicity from point view particle. As consequence, we quenched central limit theorem an algebraic rate. Furthermore, prove rate convergence for homogenization Dirichlet problems both elliptic parabolic operators.

We propose a novel actuarial risk model which, unlike the classical Crámer-Lundberg model, incorporates stream of random premiums that offset claims. A key feature is discrete time accounting and claims flow, whereby lending itself to walk type analysis. derive various estimates ruin probability thereby providing an effective method assessment over future horizon.

An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to random walk models and for a numerical evaluation of the ‘contracted path integral solution’ of the discrete master equation [Phys. Lett. A 195, 128 (1994)]. Ty...

The multifractal spectrum of discrete harmonic measure of a two dimensional simple random walk path is considered. It is shown that the spectrum is the same as for Brownian motion, is nontrivial, and can be given in terms of a quantity known as the intersection exponent.

We introduce an original way to estimate the memory parameter of elephant random walk, a fascinating discrete time walk on integers having complete its entire history. Our estimator is nothing more than quasi-maximum likelihood estimator, based second order Taylor approximation log-likelihood function. show almost sure convergence our in diffusive, critical and superdiffusive regimes. The local...