Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability
Probability
2017-05-11 v1 Mathematical Physics
Functional Analysis
math.MP
Statistics Theory
Computational Physics
Statistics Theory
Abstract
This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables. The results show that there exist the complete concentration of measure phenomenon for these mean values since the variances are all zeroes.
Cite
@article{arxiv.1705.03584,
title = {Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability},
author = {Cheng-shi Liu},
journal= {arXiv preprint arXiv:1705.03584},
year = {2017}
}
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