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/

Zendy Plus

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

Zendy Tools

Zendy Open

We study the asymptotics of Schur polynomials with partitions $\lambda$ whichare almost staircase; more precisely, partitions that differ from$((m-1)(N-1),(m-1)(N-2),\ldots,(m-1),0)$ by at most one component at thebeginning as $N\rightarrow \infty$, for a positive integer $m\ge 1$ independentof $N$. By applying either determinant formulas or integral representations forSchur functions, we show that $\frac{1}{N}\log\frac{s_{\lambda}(u_1,\ldots,u_k,x_{k+1},\ldots,x_N)}{s_{\lambda}(x_1,\ldots,x_N)}$ converges to a sum of $k$single-variable holomorphic functions, each of which depends on the variable$u_i$ for $1\leq i\leq k$, when there are only finitely many distinct $x_i$'sand each $u_i$ is in a neighborhood of $x_i$, as $N\rightarrow\infty$. Theresults are related to the law of large numbers and central limit theorem forthe dimer configurations on contracting square-hexagon lattices with certainboundary conditions.

Asymptotics of Schur functions on almost staircase partitions