Let $\boldsymbol{X}_1, \cdots, \boldsymbol{X}_{m_n}$ be independent $n\times n$ complex Ginibre ensembles and $Z_1, \cdots,$ $ Z_n$ be the eigenvalues of $\prod_{j=1}^{m_n} \boldsymbol{X}_j.$ Suppose $\lim\limits_{n\to\infty}m_n=+\infty,$ we obtain large and moderate deviations for $\max_{1\le i\le n} \log |Z_i|.$
Yutao MA
,
Chaoyang SONG
. DEVIATION PROBABILITIES FOR SPECTRAL RADIUS OF PRODUCTS OF COMPLEX GINIBRE ENSEMBLES[J]. Acta mathematica scientia, Series B, 2026
, 46(2)
: 937
-956
.
DOI: 10.1007/s10473-026-0221-3
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