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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12902 |
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| _version_ | 1866909962675945472 |
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| author | Birmpa, Panagiota Gonçalves, Patrícia Tsagkarogiannis, Dimitrios |
| author_facet | Birmpa, Panagiota Gonçalves, Patrícia Tsagkarogiannis, Dimitrios |
| contents | We consider the one-dimensional stirring process on the segment $\{-N,\ldots,N\}$, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size $K$. We investigate the non-equilibrium fluctuations of the system, starting from a product measure associated with a smooth initial profile. Given our initial state, the fluctuations are given by an Ornstein-Uhlenbeck process whose characteristic operators are the Laplacian and gradient operators. The domains of these operators include functions with boundary conditions that depend on the hydrodynamic profile. A central ingredient in our analysis is the derivation of sharp bounds on the space and space-time $v$-functions of arbitrary degree for the centered occupation variables. In particular, we prove that the $v$-functions of degree $2$ and $3$ are of order $N^{-1}$, while those of degree at least $4$ are of order $N^{-1-ζ}$ for some $ζ> 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-equilibrium fluctuations for the stirring process with births and deaths Birmpa, Panagiota Gonçalves, Patrícia Tsagkarogiannis, Dimitrios Probability We consider the one-dimensional stirring process on the segment $\{-N,\ldots,N\}$, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size $K$. We investigate the non-equilibrium fluctuations of the system, starting from a product measure associated with a smooth initial profile. Given our initial state, the fluctuations are given by an Ornstein-Uhlenbeck process whose characteristic operators are the Laplacian and gradient operators. The domains of these operators include functions with boundary conditions that depend on the hydrodynamic profile. A central ingredient in our analysis is the derivation of sharp bounds on the space and space-time $v$-functions of arbitrary degree for the centered occupation variables. In particular, we prove that the $v$-functions of degree $2$ and $3$ are of order $N^{-1}$, while those of degree at least $4$ are of order $N^{-1-ζ}$ for some $ζ> 0$. |
| title | Non-equilibrium fluctuations for the stirring process with births and deaths |
| topic | Probability |
| url | https://arxiv.org/abs/2512.12902 |