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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the Plancherel-Rotach type asymptotics of the biorthogonalpolynomials associated to the biorthogonal ensemble with the joint probabilitydensity function  \begin{equation*}  \frac{1}{C} \prod_{1 \leq i < j \leq n} (\lambda_j -\lambda_i)(f(\lambda_j) -f(\lambda_i)) \prod^n_{j = 1} W^{(n)}_{\alpha}(\lambda_j) d\lambda_j,  \end{equation*}  where  \begin{align*}  f(x) = {}& \sinh^2(\sqrt{x}), & W^{(n)}_{\alpha}(x) = {}& x^{\alpha} h(x)e^{-nV(x)}.  \end{align*}  In the special case that the potential function $V$ is linear, thisbiorthogonal ensemble arises in the quantum transport theory of disorderedwires. We analyze the asymptotic problem via $2$-component vector-valuedRiemann-Hilbert problems, and solve it under the one-cut regular with a hardedge condition.  As a consequence of our result, we observe that the equilibrium measure ofthe biorthogonal ensemble with linear $V$ is the limiting density of particlesin the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation with the ballistic initialcondition.

Biorthogonal polynomials related to quantum transport theory of disordered wires