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

In this paper we consider a finite state time discrete Markov chain that mimic the behaviour of solutions of the stochastic differential equation $$\begin{aligned} X_{t}^{\varepsilon }(x)=x-\int _0^t U^{\prime }(X_{s}^{\varepsilon })\, \mathrm {d}s+\varepsilon L_{t}, \end{aligned}$$Xtε(x)=x-∫0tU′(Xsε)ds+εLt,where U is a multi-well potential with $$n\ge 2$$n≥2 local minima and $$L=(L_t)_{t\ge 0}$$L=(Lt)t≥0 is a symmetric $$\alpha $$α-stable Lévy process (Lévy flights process). We investigate the spectrum of the generator of this Markov chain in the limit $$\varepsilon \rightarrow 0$$ε→0 and localize the top n eigenvalues $$\lambda ^\varepsilon _1,\ldots ,\lambda ^\varepsilon _n$$λ1ε,…,λnε. These eigenvalues turn out to be of the same algebraic order $$\mathcal O(\varepsilon ^\alpha )$$O(εα) and are well separated from the rest of the spectrum by a spectral gap. We also determine the limits $$\lim _{\varepsilon \rightarrow 0}\varepsilon ^{-\alpha } \lambda ^\varepsilon _i$$limε→0ε-αλiε, $$1\le i\le n$$1≤i≤n, and show that the corresponding eigenvectors are approximately constant over the domains which correspond to the potential wells of U.

Spectral Analysis for a Discrete Metastable System Driven by Lévy Flights