6533b835fe1ef96bd12a00e9

RESEARCH PRODUCT

Analysis of random walks on a hexagonal lattice

Antonio Di CrescenzoBarbara MartinucciSerena SpinaClaudio Macci

subject

Random walk01 natural sciences010104 statistics & probabilityModerate deviations0103 physical sciencesFOS: MathematicsHexagonal latticeHexagonal latticeProbability-generating functionStatistical physics0101 mathematics010306 general physicsBrownian motionMathematicsStochastic processApplied MathematicsProbability (math.PR)Random walkSymmetry (physics)Random walk; Hexagonal lattice; Probability generating function; Large deviations; Moderate deviations; First-passage timeSettore MAT/06 - Probabilita' e Statistica MatematicaLarge deviationsProbability generating functionLarge deviations theoryFirst-hitting-time modelMathematics - Probability60J15 60F10 82C41First-passage time

description

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.

yearjournalcountryeditionlanguage
2019-01-01
http://arxiv.org/abs/1610.09310