English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a substitute for the matrix product ansatz for Asymmetric SimpleExclusion Process with open boundary in the ``singular case''$\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix productansatz of Derrida, Evans, Hakim and Pasquier does not apply. In our approach,the matrix product ansatz is replaced with a pair of linear functionals on anabstract algebra. One of the functionals, $\varphi_1$, is defined on the entirealgebra, and determines stationary probabilities for large systems on $L\geqN+1$ sites. The other functional, $\varphi_0$, is defined only on afinite-dimensional linear subspace of the algebra, and determines stationaryprobabilities for small systems on $L< N+1$ sites. Functional $\varphi_0$vanishes on non-constant Askey-Wilson polynomials and in non-singular casebecomes an orthogonality functional for the Askey-Wilson polynomials.

On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case