In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on selecting an appropriate biased distribution. While an exponential tilt in the observable stands as the conventional choice for various problems, its efficiency in the context of counting statistics may be significantly hindered by the genuine discreteness of the observable. To address this challenge, we propose an alternative strategy, which we call importance sampling with the local tilt. We demonstrate the efficiency of the proposed approach through the analysis of three prototypical examples: a set of independent Gaussian random variables, Dyson gas, and symmetric simple exclusion process with a steplike initial condition.
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7 August 2024
Research Article|
August 06 2024
Importance sampling for counting statistics in one-dimensional systems
Special Collection:
Monte Carlo methods, 70 years after Metropolis et al. (1953)
Ivan N. Burenev
;
Ivan N. Burenev
a)
(Conceptualization, Formal analysis, Software, Visualization, Writing – original draft, Writing – review & editing)
LPTMS, CNRS, Université Paris-Saclay
, 91405 Orsay, France
a)Author to whom correspondence should be addressed: inburenev@gmail.com
Search for other works by this author on:
Satya N. Majumdar
;
Satya N. Majumdar
(Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing)
LPTMS, CNRS, Université Paris-Saclay
, 91405 Orsay, France
Search for other works by this author on:
Alberto Rosso
Alberto Rosso
(Conceptualization, Formal analysis, Visualization, Writing – original draft, Writing – review & editing)
LPTMS, CNRS, Université Paris-Saclay
, 91405 Orsay, France
Search for other works by this author on:
a)Author to whom correspondence should be addressed: inburenev@gmail.com
J. Chem. Phys. 161, 054115 (2024)
Article history
Received:
May 30 2024
Accepted:
July 19 2024
Citation
Ivan N. Burenev, Satya N. Majumdar, Alberto Rosso; Importance sampling for counting statistics in one-dimensional systems. J. Chem. Phys. 7 August 2024; 161 (5): 054115. https://doi.org/10.1063/5.0221076
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