We consider the random evolution described by motion of a particle moving on circle alternating angular velocities ±c and changing rotation at Poisson times, resulting in telegraph process over circle. study analytic properties semigroup it generates as well its probability distribution. The asymptotic behavior wrapped is also discussed terms circular Brownian motion. Besides, possible to deriv...

In a circle (an S 1) with circumference 1 assume m objects distributed pseudo-randomly. In the univeral covering manifold R 1 assume the objects replicated accordingly , and take an interval L > 1. In this interval, make the normalized his-togram of the pair separations which are not an integer. The theoretical (expected) such histogram is obtained in this report, as well as its difference to a...