Probabilistic Methods in Discrete Mathematics

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This book explores various advanced topics in probability theory and statistics, showcasing contributions from Russian mathematicians. It covers urn models, random forests, and the asymptotic properties of random interval graphs, highlighting their applications in cluster analysis. The work delves into the characteristics of nodes in random trees, the number field sieve, and operator equations for runs in random sequences. Additionally, it examines the limit distribution of leaf heights in plane planted trees and the weights of random Reed-Muller codewords. The text addresses limit theorems for branching processes with immigration, generalized non-ordinary Cox processes, and queue lengths in bulk arrival scenarios. It includes statistical analyses of renewal processes and functional limit theorems for stochastic observations. The distribution of vertices in plane planted forests and empty cell counts in grouped particle allocations are also discussed. Further topics include the deviation estimates of r-independent random variables from normal distribution, permutations of objects with cycle constraints, and bounds for large deviations in random vectors. The book also touches on computer security systems, waiting times in Markov-Pólya urn models, and the structure of stratified populations. Other areas include discrete distributions in control problems, Monte-Carlo estimations, and the behavior of hyperforests. The text concl