We establish modified logarithmic Sobolev inequalities for the path distrib
utions of some continuous time random walks on graphs, including the simple
examples of the discrete cube and the lattice ZZ(d). Our approach is based
on the Malliavin calculus on Poisson spaces developed by J. Picard and sto
chastic calculus. The inequalities we prove are well adapted to describe th
e tail behaviour of various functionals such as the graph distance in this
setting.