Discrete Mathematics & Theoretical Computer Science, Vol 12, No 2 (2010)

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Non Unitary Random Walks

Philippe Jacquet


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 s0, 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.

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