Mathematicians from the California Institute of Technology have solved an old problem related to a mathematical process called a random walk. The team, which also worked with a colleague from ...

The distributions of random walk quantities like ascending ladder heights and the maximum are shown to be phase-type provided that the generic random walk increment X has difference structure X = U - ...

The corresponding problem of random walk on a general Riemannian manifold is also attacked. It is shown that commutability does not hold in general, but that it does hold in completely harmonic spaces ...

Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In ...