We consider Glauber dynamics on finite cycles. By introducing a vacuum state we consider an algebraic probability space for the generator of the dynamics. We obtain a quantum decomposition of the generator and construct an interacting Fock space. As a result we obtain a distribution of the generator in the vacuum state. We also discuss the monotonicity of the moments of spectral measure as the couplings increase. In particular, when the couplings are assumed to be uniform, as the cycle grows to an infinite chain, we show that the distribution (under suitable dilation and translation) converges to a Kesten distribution.
|Journal||Infinite Dimensional Analysis, Quantum Probability and Related Topics|
|Publication status||Published - 2015 Mar 25|
Bibliographical noteFunding Information:
The research by H. J. Y. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2013285).
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics