This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C^*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.
For a Markov chain {Xj} with general state space S and f:S→Rd, the large deviation principle for {n−1 ∑j=1nf(Xj)} is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence ...
... 2013 Robert J. Buckingham and Peter D. Miller, The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates, 2013 Matthias Aschenbrenner and Stefan Friedl, 3-Manifold Groups Are Virtually Residually p, ...
A study of large deviations for empirical measures and vector-valued additive functionals of general state space Markov chains.
A completely different approach was proposed by Ney and Nummelin [NN87a, NN87b], who evaluate the LDP for additive functionals of Markov chains, and hence need to consider mainly real valued random variables, even for Markov chains ...
We do not cover large deviations theory for additive functionals of Markov chains despite the recent advances made in this field in the work of Balaji and Meyn (2000) and Kontoyiannis and Meyn (2005). Similarly, significant progress has ...
Moderate deviations for m-dependent random variables with Banach space values. ... On additive functionals of Markov chains. J. Theor. Probab. 8 905–919. . Dembo, A. and Zeitouni, O. (1993). Large Deviations Techniques and Applications.
21 ( 1993 ) 216-231 [ 9 ] Dinwoodie , I. H. and Ney , P .: Occupation measures for Markov Chains ; J. of Th ... 29 ( 1976 ) 389-461 [ 11 ] Jain , N. C .: Large deviation lower bounds for additive functionals of Markov processes ...
W. Bryc and A. Dembo, Large deviations for quadratic functionals of Gaussian processes, Preprint (1998) 3. W. Bryc and A. Dembo, On large deviations ... vector valued additive functionals of a Markov process: lower bound. Ann. Probab.
R.M. Burton and H. Dehling: Large deviations for some weakly dependent random processes, Statist. Proba. Letter, 9(1990), 397–401. 5. A. de Acosta, Large deviations for vector valued additive functionals of a Markov process: lower bound ...
MR1707339 Olle Häggström, Random-cluster representations in the study of phase transitions, Markov Process. ... MR517873 Naresh C. Jain, Large deviation lower bounds for additive functionals of Markov processes, Ann. Probab.