This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the ke...
This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer...
Statistical mechanics and its applicationsI. Gialampoukidis, K. Gustafson and I. Antoniou, Time operator of Markov chains and mixing times. Applications to financial data, Physica A 415 (2014), 141-155Gialampoukidis, I.; Gustafson, K.; Antoniou, I. Time Operator of Markov Chains and ...
advancedtechniquesforanalyzingthemixingtimesoffinitestateMarkovchainsaswellasotherrelatedtopics.Itwillmeet4hoursaweek.MathematicsDepartmentTeachers:JeffreySteif(Courseleaderandmaincontact)TimoHirscherExaminer:JeffreySteifFacultyofScience;DepartmentofMathematicalSciencesMixingTimesforMarkovChains(Part2),71/2hpThirdcycle...
Summary: In the past few years we have seen a surge in the theory of finite Markov chains, by way of new techniques to bounding the convergence to stationarity. This includes functional techniques such as logarithmic Sobolev and Nash inequalities, refined spectral and entropy techniques, and isope...
Though a chain of length 10,000 was sufficient for mixing in the simpler problem, it is insufficient for mixing when just one more constraint is required. We also ran multiple chains of length 100,000 to examine whether chains that are 10 times longer would mix. However, the longer chains...
A particular algorithm that generates non-reversible Markov processes, event-chain Monte Carlo, has led to spectacular speedups of local Markov chains in statistical physics33. In molecular systems, short- and long-range potentials are handled without any cutoffs or discretizations and, as we show ...
We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Ra...
Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Chichester, West Sussex, 1994.mixing_time(cutoff=0.25, jump=1, p=None)Return the mixing time, defined as the number of steps needed to have | p T n − π | < 0.25 , where π is the steady...