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Disordered Schur Measures

Jonathan Novak

Abstract

In this paper, we introduce and study random Schur measures whose parameters are sampled from the Circular Unitary Ensemble. We show that Schur measures with CUE disorder exhibit behavior reminiscent of spin glasses.

Disordered Schur Measures

Abstract

In this paper, we introduce and study random Schur measures whose parameters are sampled from the Circular Unitary Ensemble. We show that Schur measures with CUE disorder exhibit behavior reminiscent of spin glasses.

Paper Structure

This paper contains 13 sections, 12 theorems, 109 equations.

Table of Contents

  1. Schur Measures
  2. Partitions and particles
  3. Schur measures
  4. Cyclotomic Schur measures
  5. Schur Measures with CUE Disorder
  6. Expectations of $Z_N$ and $\log Z_N$
  7. Moments of $Z_N$
  8. Limit of $\log Z_N$
  9. Extensive Scaling
  10. Extensive free energy
  11. Variance of $\log Z_N$
  12. Self-averaging
  13. Fluctuations

Key Result

Theorem 2.1

We have and $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (21)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof
  • Theorem 3.1
  • proof
  • ...and 11 more