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Random walks and random forests

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1875)

Abstract

This chapter is inspired by the following quotation from Harris’s 1952 paper [193, §6]: Walks and trees. Random walks and branching processes are both objects of considerable interest in probability theory. We may consider a random walk as a probability measure on sequences of steps-that is, on “walks”. A branching process is a probability measure on “trees”. The purpose of the present section is to show that walks and trees are abstractly identical objects and to give probabilistic consequences of this correspondence. The identity referred to is nonprobabilistic and is quite distinct from the fact that a branching process, as a Markov process, may be considered in a certain sense to be a random walk, and also distinct from the fact that each step of the random walk, having two possible directions, represents a twofold branching.

Keywords

  • Random Forest
  • Random Graph
  • Component Size
  • Brownian Bridge
  • Plane Forest

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2006 Springer-Verlag Berlin/Heidelberg

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Pitman, J. (2006). Random walks and random forests. In: Picard, J. (eds) Combinatorial Stochastic Processes. Lecture Notes in Mathematics, vol 1875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34266-4_7

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