The critical disordered pinning measure
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909972747517952 |
|---|---|
| author | Wei, Ran Yu, Jinjiong |
| author_facet | Wei, Ran Yu, Jinjiong |
| contents | In this paper, we study a disordered pinning model induced by a random walk whose increments have a finite $(2+κ)$-th moment for some $κ>0$. It is known that this model is marginally relevant, and moreover, it undergoes a phase transition in an intermediate disorder regime. We show that, in the critical window, the point-to-point partition functions converge to a unique limiting random measure, which we call the critical disordered pinning measure. We also obtain an analogous result for a continuous counterpart to the pinning model, which is closely related to two other models: one is a critical stochastic Volterra equation that gives rise to a rough volatility model, and the other is a critical stochastic heat equation with multiplicative noise that is white in time and delta in space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The critical disordered pinning measure Wei, Ran Yu, Jinjiong Probability Mathematical Finance In this paper, we study a disordered pinning model induced by a random walk whose increments have a finite $(2+κ)$-th moment for some $κ>0$. It is known that this model is marginally relevant, and moreover, it undergoes a phase transition in an intermediate disorder regime. We show that, in the critical window, the point-to-point partition functions converge to a unique limiting random measure, which we call the critical disordered pinning measure. We also obtain an analogous result for a continuous counterpart to the pinning model, which is closely related to two other models: one is a critical stochastic Volterra equation that gives rise to a rough volatility model, and the other is a critical stochastic heat equation with multiplicative noise that is white in time and delta in space. |
| title | The critical disordered pinning measure |
| topic | Probability Mathematical Finance |
| url | https://arxiv.org/abs/2402.17642 |