Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2509.17319 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914050442526720 |
|---|---|
| author | Torri, Niccolo Wei, Ran |
| author_facet | Torri, Niccolo Wei, Ran |
| contents | This paper is a follow-up work of arxiv.org/abs/2101.05949. We study a non-directed polymer model in random environments. The polymer is represented by a simple symmetric random walk $S$ on $\mathbb{Z}^d$ with $d\geq2$ and the random environment is represented by i.i.d. heavy-tailed random variables with their tail probability decaying polynomially. We perform a Gibbs transform to describe the interaction between polymers and random environments. Up to time $N$, the law of $S$ is tilted by $\exp(\sum_{x\in\mathcal{R}_N}(βω_x-h))$, where $\mathcal{R}_N$ is the range of $S$ up to time $N$, $β\geq0$ is the inverse temperature and $h\in\mathbb{R}$ is an external field. By tuning $β=β_N$ and $h=h_N$, we establish the phase diagram and study the fluctuations of $S$ under the Gibbs transform and the scaling limits of the (logarithmic) partition function. The novelty and challenge, compared to arxiv.org/abs/2101.05949, is that we also tune the external field $h$, which brings in various range penalties, unlike in arxiv.org/abs/2101.05949, where $h$ is fixed and merely playing a role of centering for the random environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-directed polymers in random environments with range penalties: the high dimensional case Torri, Niccolo Wei, Ran Probability 82D60, 60K37, 60G70 This paper is a follow-up work of arxiv.org/abs/2101.05949. We study a non-directed polymer model in random environments. The polymer is represented by a simple symmetric random walk $S$ on $\mathbb{Z}^d$ with $d\geq2$ and the random environment is represented by i.i.d. heavy-tailed random variables with their tail probability decaying polynomially. We perform a Gibbs transform to describe the interaction between polymers and random environments. Up to time $N$, the law of $S$ is tilted by $\exp(\sum_{x\in\mathcal{R}_N}(βω_x-h))$, where $\mathcal{R}_N$ is the range of $S$ up to time $N$, $β\geq0$ is the inverse temperature and $h\in\mathbb{R}$ is an external field. By tuning $β=β_N$ and $h=h_N$, we establish the phase diagram and study the fluctuations of $S$ under the Gibbs transform and the scaling limits of the (logarithmic) partition function. The novelty and challenge, compared to arxiv.org/abs/2101.05949, is that we also tune the external field $h$, which brings in various range penalties, unlike in arxiv.org/abs/2101.05949, where $h$ is fixed and merely playing a role of centering for the random environment. |
| title | Non-directed polymers in random environments with range penalties: the high dimensional case |
| topic | Probability 82D60, 60K37, 60G70 |
| url | https://arxiv.org/abs/2509.17319 |