The first three sections give a quick overview of Martin boundary theory and state the main results. The succeeding sections will flesh out the details, and give proofs and examples. Virtually all of the results below are classical. The article Doob (1959) and the book by Kemeny, Snell, and Knapp (1976) are good sources for additional details. A recent survey article by Wolfgang Woess (1994) ha...

Epstein, R., Duberstein, P., Fenton, J., Fiscella, K., Hoerger, M., Tancredi, D., Xing, G., Gramling, R., Mohile, S., Butow, P., Walczak, A., Tattersall, M., et al (2017). Effect of a patientcentered communication intervention on oncologist-patient communication, quality of life, and health care utilization in advanced cancer: The VOICE randomized clinical trial. JAMA Oncology, 3(1), 92-100. <a...

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Λ, is classically estimated using the capacity of Λ with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices, and also t...

Consden, R., Gordon, A. H. & Martin, A. J. P. (1944). Biochem. J. 38, 224. Consden, R., Gordon, A. H. & Martin, A. J. P. (1945). Biochem. J. 39, xlvi. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946a). Biochem. J. 40, 33. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946b). Biochem. J. 40, 580. Consden, R., Gordon, A. H., Martin, A. J. P. & Synge, R. L. M. (1947). Biochem. J. 41, 596. Mar...