Along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric Hammersley's process. In the current work, we drop that assumption. We add a drift to the equation which forces solutions to remain nonnegative, and then revert to the previous proof. As a byproduct, we show the following. This is the first example of a sharp rate for a discrete walk on a continuous state space.
Probabilistic considerations give somewhat less sharp bounds for arbitrary irrationals.
To see a preprint or other information provided by the author click here . A new inequality is derived for the relative entropy of a Markov chain. This leads to a very short proof of convergence of reversible Markov chains in relative entropy. These are closely related to total variation bounds already available. However, an example shows that convergence rates in total variation and relative entropy can differ.