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日仏数学拠点FJ-LMIセミナー
過去の記録 ～11/02｜次回の予定｜今後の予定 11/03～
| 担当者 | 小林俊行, ミカエル ペブズナー |
|---|
2026年11月09日(月)
14:00-15:00 数理科学研究科棟(駒場) 123号室
Ignacio MADRID 氏 (Institute of Industrial Science, The University of Tokyo)
Explaining exclusion-like current large deviations in a single-particle diffusion-renewal system (英語)
https://fj-lmi.cnrs.fr/seminars
Ignacio MADRID 氏 (Institute of Industrial Science, The University of Tokyo)
Explaining exclusion-like current large deviations in a single-particle diffusion-renewal system (英語)
[ 講演概要 ]
In recent experiments, Henri Vo Van Qui and Nicolas Clément (LIMMS, CNRS – IIS UTokyo) measure with astonishing precision the electrical current (net electron counts over time) created by molecules diffusing independently between two electrodes, where they can repeatedly receive or release single electrons. There, in a diffusion-limited regime, we found that the electrical current fluctuations recover a characteristic noise reduction: the electron count has an asymptotic variance-to-mean ratio of 1/3. Surprisingly, this same factor appears in boundary-driven symmetric simple exclusion processes, where it is attributed to multi-particle spatial exclusion. In our case however, no exclusion occurs between molecules. In this talk we will elucidate mathematically the conditions allowing a single diffusing particle to achieve these same current fluctuations.
I will develop a stochastic model of a diffusing particle carrying a two-state mark (charged or uncharged). Its position is a reflected Brownian motion on an interval, while its charge state jumps through electron-transfer reactions governed by boundary local time. The scaled cumulant generating function of the electron count can then be obtained from an associated eigenproblem with Robin boundary conditions, for which we give a complementary probabilistic renewal description. The analysis provides a rigorous explanation of the observed noise reduction and makes explicit how it arises from the timing of diffusive round trips between the boundaries. Moreover, in the diffusion-limited regime, the correspondence with exclusion systems extends beyond the 1/3 factor to the full asymptotic counting statistics, after normalization by the mean current. The model thus provides a minimal single-particle instance of this general result, identifying diffusion and boundary-driven jumps as sufficient ingredients.
[ 講演参考URL ]In recent experiments, Henri Vo Van Qui and Nicolas Clément (LIMMS, CNRS – IIS UTokyo) measure with astonishing precision the electrical current (net electron counts over time) created by molecules diffusing independently between two electrodes, where they can repeatedly receive or release single electrons. There, in a diffusion-limited regime, we found that the electrical current fluctuations recover a characteristic noise reduction: the electron count has an asymptotic variance-to-mean ratio of 1/3. Surprisingly, this same factor appears in boundary-driven symmetric simple exclusion processes, where it is attributed to multi-particle spatial exclusion. In our case however, no exclusion occurs between molecules. In this talk we will elucidate mathematically the conditions allowing a single diffusing particle to achieve these same current fluctuations.
I will develop a stochastic model of a diffusing particle carrying a two-state mark (charged or uncharged). Its position is a reflected Brownian motion on an interval, while its charge state jumps through electron-transfer reactions governed by boundary local time. The scaled cumulant generating function of the electron count can then be obtained from an associated eigenproblem with Robin boundary conditions, for which we give a complementary probabilistic renewal description. The analysis provides a rigorous explanation of the observed noise reduction and makes explicit how it arises from the timing of diffusive round trips between the boundaries. Moreover, in the diffusion-limited regime, the correspondence with exclusion systems extends beyond the 1/3 factor to the full asymptotic counting statistics, after normalization by the mean current. The model thus provides a minimal single-particle instance of this general result, identifying diffusion and boundary-driven jumps as sufficient ingredients.
https://fj-lmi.cnrs.fr/seminars
