Scenery reconstruction with branching random walk

Abstract

We study the problem of scenery reconstruction in arbitrary dimension using observations registered in boxes of size k (for k fixed), seen along a branching random walk. We prove that, using a large enough k for almost all the realizations of the branching random walk, almost all sceneries can be reconstructed up to equivalence.

Keywords:

• random walk
• branching processes
• branching random walk

2000 Mathematics Subject Classification::

• 60J05
• 60J80

Acknowledgement

We thank the referee for his valuable comments and suggestions.

Notes

1. Email: [email protected]

Additional information

Notes on contributors

Angelica Pachon

1