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 consider particle systems (also known as point processes) on the line andin the plane, and are particularly interested in "hole" events, when there areno particles in a large disk (or some other domain). We survey the extensivework on hole probabilities and the related large deviation principles (LDP),which has been undertaken mostly in the last two decades. We mainly focus onthe recent applications of LDP-inspired techniques to the study of holeprobabilities, and the determination of the most likely configurations ofparticles that have large holes.  As an application of this approach, we illustrate how one can confirm some ofthe predictions of Jancovici, Lebowitz, and Manificat for large fluctuation inthe number of points for the (two-dimensional) $\beta$-Ginibre ensembles. Wealso discuss some possible directions for future investigations.

Point processes, hole events, and large deviations: random complex zeros and Coulomb gases