The book delves into classical combinatorial structures, exploring the intricate properties and behaviors of random graphs, permutations, and systems of random linear equations within finite fields. It presents research findings that illuminate the underlying patterns and mathematical principles governing these structures, making it a valuable resource for those interested in combinatorial theory and its applications in various fields.
Proceedings of the Third International Petrozavodsk Conference, Petrozavodsk, Russia, May 12–15, 1992
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
Proceedings of the Fourth International Petrozavodsk Conference, Petrozavodsk, Russia, June 3–7, 1996
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