Search results for Mathematics (general)

6 - Infrared Bounds
Barry Simon, California Institute of Technology
Book:

Phase Transitions in the Theory of Lattice Gases

Published online:

17 December 2025

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13 November 2025, pp 368-426
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Summary

The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.
Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.
This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

1 - Introduction
Percy Deift, New York University, Guillaume Dubach, École Polytechnique, Paris, Carlos Tomei, Pontifícia Universidade Católica do Rio de Janeiro, Thomas Trogdon, University of Washington
Book:

The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix

Published online:

24 October 2025

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13 November 2025, pp 1-15
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Summary

Our main goal is to prove the result of Deift and Trogdon (2018) on universality for the Toda eigenvalue algorithm to compute the top eigenvalue of a random real symmetric or Hermitian matrix H chosen from some random matrix ensemble. We concentrate first on the real symmetric case: The modifications that are necessary in the Hermitian case are given in Section 3.10.

Introduction
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 1-6
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Index
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 356-374
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11 - The Fundamental Theorem of Identity Types
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 144-158
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21 - The Circle
from Part III - The Circle
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 327-337
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12 - Propositions, Sets, and the Higher Truncation Levels
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 159-171
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Contents
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp v-ix
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16 - Finite Types
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 220-233
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17 - The Univalence Axiom
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 234-252
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14 - Propositional Truncations
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 193-208
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Frontmatter
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp i-iv
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4 - More Inductive Types
from Part I - Martin-Löf’s Dependent Type Theory
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 38-49
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3 - The Natural Numbers
from Part I - Martin-Löf’s Dependent Type Theory
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 29-37
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15 - Image Factorizations
from Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 209-219
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7 - Modular Arithmetic via the Curry–Howard Interpretation
from Part I - Martin-Löf’s Dependent Type Theory
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 76-93
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1 - Dependent Type Theory
from Part I - Martin-Löf’s Dependent Type Theory
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 11-19
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Acknowledgments
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp x-xii
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8 - Decidability in Elementary Number Theory
from Part I - Martin-Löf’s Dependent Type Theory
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 94-112
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Part II - The Univalent Foundations of Mathematics
Egbert Rijke, The Johns Hopkins University, Maryland
Book:

Introduction to Homotopy Type Theory

Published online:

23 October 2025

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06 November 2025, pp 113-119
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Mathematics (general)

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34925 results in Mathematics (general)

6 - Infrared Bounds

Summary

1 - Introduction

Summary

Introduction

Index

11 - The Fundamental Theorem of Identity Types

21 - The Circle

12 - Propositions, Sets, and the Higher Truncation Levels

Contents

16 - Finite Types

17 - The Univalence Axiom

14 - Propositional Truncations

Frontmatter

4 - More Inductive Types

3 - The Natural Numbers

15 - Image Factorizations

7 - Modular Arithmetic via the Curry–Howard Interpretation

1 - Dependent Type Theory

Acknowledgments

8 - Decidability in Elementary Number Theory

Part II - The Univalent Foundations of Mathematics

Mathematics (general)

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34925 results in Mathematics (general)

Summary

Summary