Constructive Neural Network Field Theory: $\phi_2^4$ in Finite Volume ESPJMBH2R2
| URI | m2://res/ESPJMBH2R2 |
|---|---|
| Kind | preprint |
| Creators | Samuel Frank |
| Date | 2026-09-30 |
| Subjects | arxiv hep-th, arxiv math-ph, arxiv math.MP |
| Scope | border |
Expressions
e1: version, preprint
| Date | 2026-09-30 |
|---|---|
| Ids | arXiv 2610.00453 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| UV convergence | statement | theorem 6.5 | arxiv |
| Commutativity of limits | statement | theorem 7.6 | arxiv |
| The free field and its shell decomposition | statement | proposition A.1 | arxiv |
| Width-uniformity of the constants | statement | lemma 7.4 | arxiv |
| Existence of the finite-width $\phi^4_2$ measure | statement | theorem 6.6 | arxiv |
| Infinite-width limit at fixed cutoff | statement | theorem 7.3 | arxiv |
| Mean identity | statement | lemma 4.8 | arxiv |
| Rarity of the bad event | statement | corollary 6.2 | arxiv |
| One-shell Hessian | statement | proposition 4.5 | arxiv |
| Free field recovery | statement | theorem A.3 | arxiv |
| Mean shift bound | statement | lemma 5.1 | arxiv |
| Quenched shell covariance | definition | definition 2.4 | arxiv |
| Quartic coercivity | statement | lemma 4.1 | arxiv |
| 6JJ87Q1FZ0 | definition | definition 3.5 | arxiv |
| Finiteness of the shell log-Laplace transform | statement | lemma 4.3 | arxiv |
| Deterministic bounds on $V_J$ and $Z_J$ | statement | lemma 2.8 | arxiv |
| Identification with the standard $\phi^4_2$ measure | statement | theorem 7.7 | arxiv |
| Width limit of the smeared field | statement | lemma 7.5 | arxiv |
| Second moment of $H_3^{(\alpha)}$ | statement | theorem 5.4 | arxiv |
| Free-field convergence in $\cC(\R^d)$ | statement | lemma 7.1 | arxiv |
| Uniform convexity | statement | corollary 4.6 | arxiv |
| Operator norm of the Gram matrix | statement | lemma 4.4 | arxiv |
| Neurons and shell field | definition | definition 2.3 | arxiv |
| Kernel convergence | statement | proposition 3.4 | arxiv |
| Increment variance | statement | lemma 2.6 | arxiv |
| Continuous convergence | statement | lemma 7.2 | arxiv |
| Concentration, uniformly over the width family | statement | lemma 3.3 | arxiv |
| Concentration | statement | theorem 3.1 | arxiv |
| Centered tilted moments | statement | corollary 4.7 | arxiv |
| Moment stability | statement | theorem 6.3 | arxiv |
| Shell dimensional analysis | statement | lemma 2.1 | arxiv |
| NXQNF8CA7Y | statement | lemma 2.9 | arxiv |
| Lower bound on the shell interaction | statement | lemma 4.2 | arxiv |
| Shell characteristic function and its width error | statement | lemma A.2 | arxiv |
| Good-field event | statement | lemma 5.3 | arxiv |
| Nested width family | definition | definition 3.2 | arxiv |
| Quenched covariance reproduces the shell kernel | statement | lemma 2.5 | arxiv |
| The finite-volume $\phi^4_2$ measure | statement | corollary 7.8 | arxiv |
| Free-field supremum tail | statement | lemma 6.1 | arxiv |
| Telescoping factor | statement | proposition 6.4 | arxiv |
| Interpolation derivative | statement | proposition 5.2 | arxiv |
| Log-Laplace bound | statement | theorem 5.5 | arxiv |
| Telescoping | statement | proposition 2.10 | arxiv |
Catalogue records
- arxiv: 2610.00453 (work)