Mixing time of an unaligned Gibbs sampler on the square

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square $[0,1]^2$ to approach a stationary distribution with density proportional to $\exp(-A^2(u-v)^2)$ for $(u,v)\in [0,1]^2$ with some large parameter $A$. Diaconis conjectured the mixing time of this process to be $O(A^2)$ which we confirm in this paper. This improves on the currently known $O(\exp(A^2))$ estimate

Integer Quantization of the Chern-Simons Coefficient in a Broken Phase

We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by $1/4\pi$ times an integer, preserving the usual integer quantization condition on the bare parameters.Comment: 9 pages LaTeX, two figures available upon reques

Индустрия 4.0

Pavlyuchuk Yu. N., Tsekanovsky Z., Novitska U. Industry 4.