Limit Theorems for the Left Random Walk on GLd (R)

Motivated by a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd ®, such as the Marcinkiewicz-Zygmund strong law of large numbers, the CLT (with rates in Wasserstein’s distances) and almost sure invariance principles with rates.