The notion of the random forest arises when we define a probability measure on a set of graphs representing forests. In this case various numerical characteristics of forests become random variables and the most convenient way to study them is to apply the probability theory methods. Formally, the random forest is a specific case of the random object, i.e. a generalization of the concept of a random variable such that its values are not real numbers, but the combinatory objects under consideration.
Random forests can be used to fulfil various applied tasks such as modelling of transport, electricity and telecommunication networks, in applied statistics and the theory of algorithms, as well as to solve problems in various fields of mathematics.
The theory of random forests is considered in detail in the book:
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Here You will find the list of publications on the theory of random forests. It has no claims for completeness. Still it includes all papers by Petrozavodsk mathematicians studying the problem, as well as the works by both Russian and foreign authors we belive essential.
The problems related to the theory of random forests are regularly discussed at traditional Petrozavodsk International Conferences "Probability Methods in Discrete Mathematics", including the last fifth one, held in 2000.