36 citations · 39 across the 3 of their papers we have counts for
5 papers · 1 filter
A Central Limit Theorem for non-overlapping return times
Oliver Johnson
Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on th…
Preservation of log-concavity on summation
Oliver Johnson, Christina Goldschmidt
We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still…
Convergence of the Poincare Constant
Oliver Johnson
The Poincare constant R(Y) of a random variable Y relates the L2 norm of a function g and its derivative g'. Since R(Y) - Var(Y) is positive, with equality if and only if Y is norm…
A conditional Entropy Power Inequality for dependent variables
Oliver Johnson
We provide a condition under which a version of Shannon's Entropy Power Inequality will hold for dependent variables. We provide information inequalities extending those found in t…
An information-theoretic Central Limit Theorem for finitely susceptible FKG systems
Oliver Johnson
We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure i…