Progress in Pure and Applied Discrete Mathematics, Vol. 1: Probabilistic Methods in Discrete Mathematics

More about the book

This work presents a comprehensive overview of various topics in the theory of random mappings and their applications across multiple fields. It begins with an exploration of the early history of random mappings and delves into Goncharov's contributions to combinatorics. The text examines probability distributions in prime number theory and discusses recent developments in polynomial allocations. Key properties of random permutations, particularly regarding maximum cycle lengths, are analyzed alongside stochastic properties of random linear equations over finite algebraic structures. The book addresses security challenges in information processing systems and presents decomposable statistics based on spacings. It further investigates allocation processes with specified frequency vector distributions and statistical estimation of radioactive waste compositions. Transient phenomena in branching migration processes and the asymptotic behavior of waiting times in particle allocation schemes are also covered. Limit theorems for U-statistics and decomposable statistics of dependent random variables are discussed, alongside methods for estimating finite stratified populations. The text includes asymptotic expansions for permutation tests and examines lower bounds for isoperimetric numbers in cubic graphs. Additionally, it explores phase transitions in random graphs, random Euclidean mappings, and percolation methods. The work concl