# Non Unitary Random Walks

1 HIPERCOM - High performance communication
Inria Paris-Rocquencourt, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : 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.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 12 (2), pp.333-362

Littérature citée [12 références]

https://hal.inria.fr/hal-00994977
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : jeudi 22 mai 2014 - 14:25:23
Dernière modification le : vendredi 25 mai 2018 - 12:02:06
Document(s) archivé(s) le : vendredi 22 août 2014 - 12:30:58

### Fichier

1349-5118-2-PB.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-00994977, version 1

### Citation

Philippe Jacquet. Non Unitary Random Walks. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 12 (2), pp.333-362. 〈hal-00994977〉

### Métriques

Consultations de la notice

## 319

Téléchargements de fichiers