%0 Book Section %1 csp-rwf %A Pitman, Jim %B Combinatorial Stochastic Processes %D 2006 %I Springer-Verlag %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley branching_process random_trees_and_forests random_walk myown %P 121--141 %T Random walks and random forests %U http://dx.doi.org/10.1007/3-540-34266-4_7 %V 1875 %X This chapter is inspired by the following quotation from Harris's 1952 paper on random 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 two fold branching. %& 7

@inbook{csp-rwf, abstract = {This chapter is inspired by the following quotation from Harris's 1952 paper on random walks and trees. {\em 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 two fold branching}.}, added-at = {2008-01-21T00:31:04.000+0100}, author = {Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/2d1db9a93b60ef5d21569e232d71ac811/pitman}, booktitle = {Combinatorial Stochastic Processes}, chapter = 7, description = {SpringerLink - Book Chapter}, interhash = {80033db2ea94760a7382181edda04bf7}, intrahash = {d1db9a93b60ef5d21569e232d71ac811}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley branching_process random_trees_and_forests random_walk myown}, pages = {121--141}, publisher = {Springer-Verlag}, series = {Lecture Notes in Mathematics}, timestamp = {2010-10-30T22:51:59.000+0200}, title = {Random walks and random forests}, url = {http://dx.doi.org/10.1007/3-540-34266-4_7}, volume = 1875, year = 2006 }