Correlated and uncorrelated long-time asymptotics of type D ASEP: formalization blueprint
Conventions
1
The model and exact structure
2
Kernel theory (paper §4–5)
3
The Edwards–Wilkinson regime (paper §6)
4
The initial-condition crossover (paper §7)
5
The Tracy–Widom regime (paper §8)
6
The Skorokhod space \(D([0,1],\mathbb {R})\)
▶
6.1
The space and Billingsley’s metric \(d^\circ \)
6.2
The càdlàg modulus \(w'\)
6.3
Completeness and Polishness
6.4
Compactness, the sup-norm, and the tightness bridge
6.5
Measurability: evaluations and the cylinder \(\sigma \)-algebra
6.6
Aldous’s criterion
7
Nuclear structure of \(\mathcal{S}(\mathbb {R})\) and Mitoma’s criterion
▼
7.1
The Fréchet package for \(\mathcal{S}(\mathbb {R})\)
7.2
Separability and the countable dense set
7.3
The pointwise dual and compact polar balls
7.4
Hermite functions and the Hilbert basis of \(L^2(\mathbb {R})\)
7.5
The Hermite–Sobolev chain
7.6
The probabilistic core: Mitoma confinement
Dependency graph
7 Nuclear structure of \(\mathcal{S}(\mathbb {R})\) and Mitoma’s criterion
7.1
The Fréchet package for \(\mathcal{S}(\mathbb {R})\)
7.2
Separability and the countable dense set
7.3
The pointwise dual and compact polar balls
7.4
Hermite functions and the Hilbert basis of \(L^2(\mathbb {R})\)
7.5
The Hermite–Sobolev chain
7.6
The probabilistic core: Mitoma confinement