Nonconventional Limit Theorems and Random Dynamics

The book is devoted to limit theorems for nonconventional sums and arrays. Asymptotic behavior of such sums were first studied in ergodic theory but recently it turned out that main limit theorems of probability theory, such as central, local and Poisson limit theorems can also be obtained for such expressions. In order to obtain sufficiently general local limit theorem, we develop also thermodynamic formalism type results for random complex operators, which is one of the novelties of the book.

Contents:

• Nonconventional Limit Theorems:

  • Stein's Method for Nonconventional Sums
  • Local Limit Theorem
  • Nonconventional Arrays
  • Random Transformations

• Thermodynamic Formalism for Random Complex Operators:

  • Ruelle–Perron–Frobenius Theorem via Cone Contractions
  • Application to Random Locally Expanding Covering Maps
  • Pressure, Asymptotic Variance and Complex Gibbs Measures
  • Application to Random Complex Integral Operators
  • Fiberwise Limit Theorems

Readership: Advanced graduate students and researchers in probability theory and stochastic processes and dynamical systems and ergodic theory.
Key Features:

• The results in the book are new and never appeared before, Prof. Yuri Kifer is a well-known researcher in probability and dynamical systems, he published several books and more than 130 papers and he initiated the research on nonconventional limit theorems in the last decade