An outline of the theory of stationary measures over ℝq

1980 ◽  
pp. 295-309
Author(s):  
P. Masani
Keyword(s):  
Stationary Measures

Convergence to stationary measures in nonlinear Fokker—Planck—Kolmogorov equations

2018 ◽  
Vol 482 (4) ◽  
pp. 369-374
Author(s):  
V. Bogachev ◽  
◽  
M. Roeckner ◽  
S. Shaposhnikov ◽  
◽  
...  
Keyword(s):  
Kolmogorov Equations ◽  
Stationary Measures ◽  
Fokker Planck

The non-uniform stationary measure for discrete-time quantum walks in one dimension

2015 ◽  
Vol 15 (11&12) ◽  
pp. 1060-1075
Author(s):  
Norio Konno ◽  
Masato Takei
Keyword(s):  
Eigenvalue Problem ◽  
Discrete Time ◽  
Quantum Walks ◽  
Stationary Measure ◽  
Unitary Matrix ◽  
Uniform Measure ◽  
Simple Argument ◽  
Stationary Measures ◽  
Time Quantum ◽  
The One

We consider stationary measures of the one-dimensional discrete-time quantum walks (QWs) with two chiralities, which is defined by a 2 $\times$ 2 unitary matrix $U$. In our previous paper \cite{Konno2014}, we proved that any uniform measure becomes the stationary measure of the QW by solving the corresponding eigenvalue problem. This paper reports that non-uniform measures are also stationary measures of the QW except when $U$ is diagonal. For diagonal matrices, we show that any stationary measure is uniform. Moreover, we prove that any uniform measure becomes a stationary measure for more general QWs not by solving the eigenvalue problem but by a simple argument.

scholarly journals Pseudo-orbits, stationary measures and metastability

2014 ◽  
Vol 29 (3) ◽  
pp. 322-336 ◽  
Author(s):  
Wael Bahsoun ◽  
Huyi Hu ◽  
Sandro Vaienti
Keyword(s):  
Stationary Measures

scholarly journals Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus

2011 ◽  
Vol 24 (1) ◽  
pp. 231-231 ◽  
Author(s):  
Jean Bourgain ◽  
Alex Furman ◽  
Elon Lindenstrauss ◽  
Shahar Mozes
Keyword(s):  
Stationary Measures
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