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Exact and Efficient Sampling of Conditioned Walks
Authors:Matteo Adorisio  Alberto Pezzotta  Clélia de Mulatier  Cristian Micheletti  Antonio Celani
Affiliation:1.Scuola Internazionale Superiore di Studi Avanzati (SISSA),Trieste,Italy;2.The Abdus Salam International Centre for Theoretical Physics (ICTP),Trieste,Italy
Abstract:A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.
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