### Non Unitary Random Walks

*Philippe Jacquet*

#### Abstract

Motivated by the recent refutation of information loss paradox in
black hole by Hawking, we investigate the new concept of

*non unitary random walks*. In a non unitary random walk, we consider that the state s_{0}, called the*black hole*, has a probability weight that decays exponentially in e^{-λt}for some λ>0. This decaying probabilities affect the probability weight of the other states, so that the the apparent transition probabilities are affected by a repulsion factor that depends on the factors λ and black hole lifetime t. If λ is large enough, then the resulting transition probabilities correspond to a neutral random walk. We generalize to*non unitary gravitational walks*where the transition probabilities are function of the distance to the black hole. We show the surprising result that the black hole remains attractive below a certain distance and becomes repulsive with an exactly reversed random walk beyond this distance. This effect has interesting analogy with the so-called dark energy effect in astrophysics.Full Text: PDF PostScript