B. Tsirelson

Trees, not cubes...

Recent works

Oded Schramm and Boris Tsirelson,
"Trees, not cubes: hypercontractivity, cosiness, and noise stability."
Electronic Communication in Probability 4:6, 39-49 (1999).
Available online (free of charge) from the main site (USA):
or its Israeli mirror:

A short (11 pages, 3 figures) research paper. Bibl. 14 refs.

Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.

  1. Introduction.
  2. Stability and sensitivity on cubes, revisited.
  3. Stability and sensitivity on trees.
  4. Hypercontractivity.
  5. The main result.
  6. Connections to continuous models.
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