A new approach to strong embeddings

Details A new approach to strong embeddings A new approach to strong embeddings

2007-11-04

arxiv.org/abs/0711.0501v3

Mathematics

Probability

A new example has been added. To appear in PTRF. 31 pages

Scientific paper

We revisit strong approximation theory from a new perspective, culminating in a proof of the Koml\'os-Major-Tusn\'ady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy inequalities. The new technique, inspired by Stein's method of normal approximation, is applicable to any setting where Stein's method works. In particular, one can hope to take it beyond sums of independent random variables.

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