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 substantially refine asymptotic logarithmic upper bounds produced by Svante Janson (2015) on the right tail of the limiting QuickSort distribution function F and by Fill and Hung (2018) on the right tails of the corresponding density f and of the absolute derivatives of f of each order. For example, we establish an upper bound on log[1 − F (x)] that matches conjectured asymptotics of Knessl and Szpankowski (1999) through terms of order (log x); the corresponding order for the Janson (2015) bound is the lead order, x log x. Using the refined asymptotic bounds on F , we derive right-tail large deviation (LD) results for the distribution of the number of comparisons required by QuickSort that substantially sharpen the two-sided LD results of McDiarmid and Hayward (1996).

QuickSort: Improved right-tail asymptotics for the limiting distribution, and large deviations (Extended Abstract)