Eigenvalues and Mixing Time
نویسنده
چکیده
Mixing time of a Markov chain depends on the eigenvalues of its transition matrix. We give some examples and bounds on the mixing time in terms of the eigenvalue having second largest absolute value. This paper is based on Chapters 1, 4, and 12 of [1].
منابع مشابه
Eigenvalues of non-reversible Markov chains: their connection to mixing times, reversible Markov chains, and Cheeger inequalities
We show a lower bound on mixing time for a non-reversible Markov chain in terms of its eigenvalues. This is used to show a bound on the real part of the complex-valued eigenvalues in terms of the realvalued eigenvalues of a related reversible chain, and likewise to bound the second largest magnitude eigenvalue. A myriad of Cheeger-like inequalities also follow for non-reversible chains, which e...
متن کاملLocalization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix
This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center and radius. This new algorithm ca...
متن کاملLow-lying Wilson Dirac operator eigenvector mixing in dynamical overlap hybrid Monte Carlo
Current dynamical overlap fermion hybrid Monte Carlo simulations encounter large fermionic forces when there is mixing between eigenvectors of the kernel operator with near zero-eigenvalues. This leads to low acceptance rates when there is a large density of near zero eigenvalues. I present a method where these large forces are eliminated and the large action jumps seen when two eigenvalues app...
متن کاملFluid Dynamics in a Copper Converter: an Investigation on Mixing Phenomena in an Experimental Model
In this study, the mixing phenomena and fluid dynamics in a copper converter have been experimentally investigated using a physical model. The physical model is a 1:5 horizontal tank made of Plexiglas. The mixing phenomena have been characterized by experimentally measuring the mixing time using a tracer dispersion technique. Moreover, the effects of the air flow rate and lance submergence on t...
متن کاملThe Eigenvalue Gap and Mixing Time
The eigenvalue or spectral gap of a Markov chain is the difference between the two largest eigenvalues of the transition matrix of its underlying (state space) graph. In this paper we explore the intimate relationship between the spectral gap of a Markov chain and its mixing time, as well as another closely related structural property of a Markov chain known as conductance. The relationships am...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013