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'Et moi, ..., si j' avait su comment en revenir, One service
mathematics has rendered the human race. It has put common sense
back je n'y serais point aIle.' Jules Verne where it belongs, on
the topmost shelf next to the dusty canister labelled 'discarded
non- The series is divergent; therefore we may be sense'" able 10
do something with it. Eric T. Bell O. Heaviside Mathematics is a
tool for thought. A highly necessary tool in a world where both
feedback and non linearities abound_ Similarly, all kinds of parts
of mathematics serve as tools for other parts and for other
sciences. Applying a simple rewriting rule to the quote on the
right above one finds such statements as: 'One service topology has
rendered mathematical physics .. .'; 'One service logic has
rendered com puter science .. .'; 'One service category theory has
rendered mathematics .. .'. All arguably true. And all statements
obtainable this way form part of the raison d'etre of this series."
New and striking results obtained in recent years from an intensive
study of asymptotic combinatorics have led to a new, higher level
of understanding of related problems: the theory of integrable
systems, the Riemann-Hilbert problem, asymptotic representation
theory, spectra of random matrices, combinatorics of Young diagrams
and permutations, and even some aspects of quantum field theory.
New and striking results obtained in recent years from an intensive
study of asymptotic combinatorics have led to a new, higher level
of understanding of related problems: the theory of integrable
systems, the Riemann-Hilbert problem, asymptotic representation
theory, spectra of random matrices, combinatorics of Young diagrams
and permutations, and even some aspects of quantum field theory.
'Et moi, ..., si j' avait su comment en revenir, One service
mathematics has rendered the human race. It has put common sense
back je n'y serais point aIle.' Jules Verne where it belongs, on
the topmost shelf next to the dusty canister labelled 'discarded
non- The series is divergent; therefore we may be sense'" able 10
do something with it. Eric T. Bell O. Heaviside Mathematics is a
tool for thought. A highly necessary tool in a world where both
feedback and non linearities abound_ Similarly, all kinds of parts
of mathematics serve as tools for other parts and for other
sciences. Applying a simple rewriting rule to the quote on the
right above one finds such statements as: 'One service topology has
rendered mathematical physics .. .'; 'One service logic has
rendered com puter science .. .'; 'One service category theory has
rendered mathematics .. .'. All arguably true. And all statements
obtainable this way form part of the raison d'etre of this series."
Markov chains are an important idea, related to random walks, which
crops up widely in applied stochastic analysis. They are used for
example in performance modeling and evaluation of computer
networks, queuing networks, and telecommunication systems. The main
point of the present book is to provide methods, based on the
construction of Lyapunov functions, of determining when a Markov
chain is ergodic, null recurrent, or transient. These methods,
which are on the whole original and new, can also be extended to
the study of questions of stability. Of particular concern are
reflected random walks and reflected Brownian motion. Here, the
authors provide a self-contained introduction to the theory and
details of how the required Lyapunov functions are constructed in
various situations.
Markov chains are an important idea, related to random walks, which
crops up widely in applied stochastic analysis. They are used for
such applications as performance modelling and evaluation of
computer networks, queuing networks and telecommunication systems.
The point of this book is to provide methods, based on the
construction of Lyapunov functions, of determining when a Markov
chain is ergodic, null recurrent or transient. These methods, which
are, on the whole, original and new, can also be extended to the
study of questions of stability. Of particular concern are
reflected random walks and reflected Brownian motion. The authors
provide not only a self-contained introduction to the theory, but
also details of how the required Lyapunov functions are constructed
in various situations.
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