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Path probability for a Brownian motion |
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| Authors: | TongLing Lin Cyril Pujos CongJie Ou WenPing Bi Florent Calvayrac Qiuping Alexandre Wang |
| Affiliation: | LIN TongLing1,2,PUJOS Cyril1,OU CongJie3,BI WenPing4,CALVAYRAC Florent2 & WANG Qiuping Alexandre1,2 1 LUNAM Université,ISMANS,Laboratoire de Physique Statistique et Systèmes Complexes,44,Avenue F.A. Bartholdi,72000 Le Mans,France,2 LPEC,Université du Maine,Ave. O. Messiaen,72035 Le Mans,3 College of Information Science and Engineering,Huaqiao University,Quanzhou 362021,China,4 Laboratoire d'Acoustique,72085 Le Mans Cedex 9 |
| Abstract: | This work reports on numerical simulations of Brownian motion in the non-dissipative limit. The objective was to prove the existence of path probability and to compute probability values for some sample paths. By simulating a large number of particles moving from point to point under Gaussian noise and conservative forces, we numerically determine that the path probability decreases exponentially with increasing Lagrangian action of the paths. |
| Keywords: | classical Brownian motion path probability Lagrangian action Hamiltonian action |
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