Nonconventional random matrix products

Yuri Kifer, Sasha Sodin

Research output: Contribution to journalArticlepeer-review


Let ξ1, ξ2, … be independent identically distributed random variables and F: ℝl → SLd(ℝ) be a Borel measurable matrix-valued function. Set Xn = F(ξq1(n), ξq2(n), …, ξql(n)) where 0 ≤ q1 < q2 < … < ql are increasing functions taking on integer values on integers. We study the asymptotic behavior as N → ∞ 1 of the singular values of the random matrix product ΠN = XN … X2X1 and show, in particular, that (under certain conditions) [math] converges with probability one as N → ∞. We also obtain similar results for such products when ξi form a Markov chain. The essential difference from the usual setting appears since the sequence (Xn, n ≥ 1) is long-range dependent and nonstationary.

Original languageEnglish
JournalElectronic Communications in Probability
StatePublished - 2018
Externally publishedYes


FundersFunder number
Spectrum Pharmaceuticals
Horizon 2020 Framework Programme639305
Royal Society
Wolfson College, University of Oxford
European Research Council


    • Avalanche principle
    • Large deviations
    • Nonconventional limit theorems
    • Random matrix products


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