## Philippe Jacquet - Non Unitary Random Walks

dmtcs:480 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, Vol. 12 no. 2 - https://doi.org/10.46298/dmtcs.480
Non Unitary Random Walks

Authors: Philippe Jacquet

Motivated by the recent refutation of information loss paradox in black hole by Hawking, we investigate the new concept of {\it non unitary random walks}. In a non unitary random walk, we consider that the state 0, called the {\it black hole}, has a probability weight that decays exponentially in $e^{-\lambda t}$ for some $\lambda>0$. 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 $\lambda$ and black hole lifetime $t$. If $\lambda$ is large enough, then the resulting transition probabilities correspond to a neutral random walk. We generalize to {\it 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 so-called dark energy effect in astrophysics.

Volume: Vol. 12 no. 2
Published on: January 1, 2009
Imported on: March 26, 2015
Keywords: ACM : ,ACM : ,ACM : ,[INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI]