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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $(g_n)_{n\geq 1}$ be a sequence of independent and identicallydistributed elements of the general linear group $GL(d, \mathbb R)$. Considerthe random walk $G_n: = g_n \ldots g_1$. Under suitable conditions, weestablish Bahadur-Rao-Petrov type large deviation expansion for thecoefficients $\langle f, G_n v \rangle$, where $f \in (\mathbb R^d)^*$ and $v\in \mathbb R^d$. In particular, our result implies the large deviationprinciple with an explicit rate function, thus improving significantly thelarge deviation bounds established earlier. Moreover, we establishBahadur-Rao-Petrov type large deviation expansion for the coefficients $\langlef, G_n v \rangle$ under the changed measure. Toward this end we prove theH\"{o}lder regularity of the stationary measure corresponding to the Markovchain $G_n v /|G_n v|$ under the changed measure, which is of independentinterest. In addition, we also prove local limit theorems with large deviationsfor the coefficients of $G_n$.

Large deviation expansions for the coefficients of random walks on the general linear group