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 study the landscape complexity of the Hamiltonian $X_N(x) +\frac\mu2\|x\|^2,$ where $X_{N}$ is a smooth Gaussian process with isotropic incrementson $\mathbb R^{N}$. This model describes a single particle on a randompotential in statistical physics. We derive asymptotic formulas for the meannumber of critical points of index $k$ with critical values in an open set asthe dimension $N$ goes to infinity. In a companion paper, we provide the sameanalysis without the index constraint.

Complexity of Gaussian random fields with isotropic increments: critical points with given indices