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Beyond canonical decoupling

Ciprian Demeter

Abstract

We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new grounds and answers some questions.

Beyond canonical decoupling

Abstract

We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new grounds and answers some questions.
Paper Structure (4 sections, 17 theorems, 112 equations)

This paper contains 4 sections, 17 theorems, 112 equations.

Table of Contents

  1. The large ensemble problem
  2. Conjecture \ref{['c1']} implies the Restriction Conjecture
  3. An unconditional large ensemble decoupling
  4. Tight decoupling

Key Result

Theorem 1.1

For $2\le p\le 4$ we have

Theorems & Definitions (31)

  • Theorem 1.1
  • Definition 1.2
  • Conjecture 1.3: Large ensemble decoupling for the paraboloid
  • Theorem 1.4
  • proof
  • Theorem 2.1
  • Corollary 2.2
  • Corollary 2.3
  • Lemma 2.4
  • proof
  • ...and 21 more