A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts   with applications to renewal theory
  We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case. 
Mark Kesseb\"ohmer and Sabrina Kombrink
math.DS