Georgia Institute of Technology College of Sciences

Under certain conditions, we obtain exact asymptotic expressions for the stationary distribution \pi of a Markov chain.  In this talk, we will consider Markov chains on {0,1,...}^2.  We are particularly interested in deriving asymptotic expressions when the fluid limit of the most probable paths from the origin to the rare event are nonlinear.  For example, we will derive asymptotic expressions for a large deviation along the x-axis (e.g., \pi(\ell, y) for fixed y) when the most probable paths to (\ell,y) initially climb the y-axis before turning southwest and drifting towards (\ell,y).