A new approach to strong embeddings
By Sourav Chatterjee. 2007
53 citations recorded by the source corpus.
We revisit strong approximation theory from a new perspective, culminating in a proof of the Komlós–Major–Tusnády 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.
Subfields: Management Science and Operations Research, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/17edf362c1f3041cd1bb68f770121029dfce1fa6
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In Management Science and Operations Research
- Ivan Nourdin
- Michel Ledoux
- Giovanni Peccati
- Ian Waudby-Smith
- Aaditya Ramdas
- Sourav Chatterjee
- Edward H. Kennedy
- Martin J. Wainwright
In Mathematical Physics
- Ivan Nourdin
- Giovanni Peccati
- Michel Ledoux
- Sourav Chatterjee
- Aaditya Ramdas
- Gesine Reinert
- Matthias Schulte
- Lihu Xu
In Statistics and Probability
- Ivan Nourdin
- Giovanni Peccati
- Michel Ledoux
- Ian Waudby-Smith
- Edward H. Kennedy
- David T. Arbour
- Ritwik Sinha
- Aaditya Ramdas
Citations in the corpus
- A short survey of Stein's method (2014, background): “There are a number of nonstandard applications of Stein’s method that have not yet gathered a lot of follow up action, for example, Edgeworth expansions (Rinott and Rotar [73]), rates of convergence of Markov chains (Diaconis [39]), strong approximation in the style of the KMT embedding theorem (my ”
- Time-uniform central limit theory and asymptotic confidence sequences (2021, background): “2 Strassen’s strong approximation Strassen [50] initiated the study of strong approximation (also called strong invariance principles or strong embeddings) which blossomed into an active and impactful corner of probability theory research over the subsequent years, culminating in now-classical resul”
- Stein’s method, logarithmic Sobolev and transport inequalities (2014, methodology): “rithmic Sobolev inequalities are classically related to (Gaussian) concentration inequalities by means of the Herbst argument (cf. e.g. [L2, B-L-M]). Stein’s method has also been used to this task in [C3], going back however to the root of the methodology of exchangeable pairs. The basic principle e”