A Sketch of Menshikov ’ s Theorem

  title={A Sketch of Menshikov ’ s Theorem},
  author={Thomas J. Bao},
Let −→ Λ be an infinite, locally finite oriented multi-graph with C− → Λ finite and strongly connected, and let p < pH( −→ Λ ). Menshikov’s theorem states that there exists an α > 0 s.t. Pp(x n →) ≤ exp(−αn/(logn)) for all sites x and n ≥ 2. In this paper, we begin backwards, explaining the importance of this theorem and then giving a sketch of the proof, emphasizing the intuition and motivations behind the methods used. Unfortunately, due to constraints on space, we’ll sometimes simply… CONTINUE READING