The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for mathematicians and students.

Probability distributions on cladograms.- Stability of self-organizing processes.- Some examples of normal approximations by Stein's method.- Large deviations for random distribution of mass.- Random minimax game tress.- Metrics on compositions and coincidences among renewal sequences.- The no long odd cycle theorem for completely positive matrices.- A note on triangle-free graphs.- Intersections and limits of regenerative sets.- Random processes of the form Xn+1 = anXn + bn (mod p) where bn takes on a single value.- The second moment method, conditioning and approximation.- How fast and where does a random walker move on a random tree?.- A note on recurrence, amenability, and the universal cover of graphs.- On which graphs are all random walks in random environments transient?.- Energy, and intersections of Markov chains.