The semicircle law for matrices with ergodic entries

Publication date: October 2018Source: Statistics & Probability Letters, Volume 141Author(s): Matthias LöweAbstractWe study the empirical spectral distribution (ESD) of symmetric random matrices with ergodic entries on the diagonals. We observe that for entries with correlations that decay to 0, when the distance of the diagonal entries becomes large the limiting ESD is the well known semicircle law. If it does not decay to 0 (and have the same sign) the semicircle law cannot be the limit of the ESD. This is in good agreement with results on exchangeable processes analyzed in Friesen and Löwe (2013) and Hochstättler et al. (2016).

Source: Statistics and Probability Letters - July 10, 2018 Category: Statistics Source Type: research