De Bruyne Benjamin, Majumdar Satya N, Schehr Grégory
LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Phys Rev E. 2021 Aug;104(2-1):024117. doi: 10.1103/PhysRevE.104.024117.
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly accounts for the bridge constraint. It is illustrated on various jump distributions and is shown to be very efficient in practice. In addition, we show how to generalize the method to other types of constrained random walks such as generalized bridges, excursions, and meanders.
