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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We investigate here the asymptotic behaviour of a large, typical meandric system. More precisely, we show the quenched local convergence of a random uniform meandric system   $\boldsymbol {M}_n$   on   $2n$   points, as   $n \rightarrow \infty $  , towards the infinite noodle introduced by Curien  et al.  [ 3 ]. As a consequence, denoting by   $cc( \boldsymbol {M}_n)$   the number of connected components of   $\boldsymbol {M}_n$  , we prove the convergence in probability of   $cc(\boldsymbol {M}_n)/n$   to some constant   $\kappa $  , answering a question raised independently by Goulden–Nica–Puder [ 8 ] and Kargin [ 12 ]. This result also provides information on the asymptotic geometry of the Hasse diagram of the lattice of non-crossing partitions. Finally, we obtain expressions of the constant   $\kappa $   as infinite sums over meanders, which allows us to compute upper and lower approximations of   $\kappa $  .

Components in Meandric Systems and the Infinite Noodle