Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

We present a functional central limit theorem which quantifies, as a stochastic process, the difference between a PEPA model’s underlying CTMC and its fluid approximation. We generalise existing theory to handle the case of non-smooth rate functions, which is an issue particular to modelling problems in computer science. We verify the weak convergence empirically and suggest future avenues for ...

Points P1; : : : ; Pn in the unit square de ne a convex n-chain if they are below y = x and, together with P0 = (0; 0) and Pn+1 = (1; 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature is...

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure central limit theorem. We also discuss the quenched central limit th...