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Exact Fundamental Functions of the Random Walk in One‐dimensional Confined System
Author(s) -
Yoon JoungHahn,
Kim Hyojoon
Publication year - 2017
Publication title -
bulletin of the korean chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 59
ISSN - 1229-5949
DOI - 10.1002/bkcs.11093
Subject(s) - exact solutions in general relativity , random walk , boundary value problem , boundary (topology) , mathematics , mathematical analysis , statistical physics , physics , statistics
We have found the exact discrete solutions for the one‐dimensional confined system where two outer boundaries are either absorbing or reflecting. The solution can be easily generalized to the system where one boundary is absorbing and the other is reflecting. The exact solutions are proved by the mathematical induction method analytically and by the simulations numerically. We also prove that the exact discrete solution can be reduced to the well‐known continuum solution.