Exact extreme, order and sum statistics in a class of strongly correlated system
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911746075131904 |
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| author | Biroli, Marco Larralde, Hernán Majumdar, Satya N. Schehr, Grégory |
| author_facet | Biroli, Marco Larralde, Hernán Majumdar, Satya N. Schehr, Grégory |
| contents | Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and identically distributed (i.i.d) random variables $\{X_1,\, X_2,\ldots, X_N\}$ whose common distribution has a parameter $Y$ (or a set of parameters) which itself is random with its own distribution. For a fixed value of this parameter $Y$, the $X_i$ variables are independent and we call them conditionally independent and identically distributed (c.i.i.d). However, once integrated over the distribution of the parameter $Y$, the $X_i$ variables get strongly correlated, yet retaining a solvable structure for various observables, such as for the sum and the extremes of $X_i$'s. This provides a simple procedure to generate a class of solvable strongly correlated systems. We illustrate how this procedure works via three physical examples where $N$ particles on a line perform independent (i) Brownian motions, (ii) ballistic motions with random initial velocities, and (iii) Lévy flights, but they get strongly correlated via {\it simultaneous resetting} to the origin. Our results are verified in numerical simulations. This procedure can be used to generate an endless variety of solvable strongly correlated systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15351 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact extreme, order and sum statistics in a class of strongly correlated system Biroli, Marco Larralde, Hernán Majumdar, Satya N. Schehr, Grégory Statistical Mechanics Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and identically distributed (i.i.d) random variables $\{X_1,\, X_2,\ldots, X_N\}$ whose common distribution has a parameter $Y$ (or a set of parameters) which itself is random with its own distribution. For a fixed value of this parameter $Y$, the $X_i$ variables are independent and we call them conditionally independent and identically distributed (c.i.i.d). However, once integrated over the distribution of the parameter $Y$, the $X_i$ variables get strongly correlated, yet retaining a solvable structure for various observables, such as for the sum and the extremes of $X_i$'s. This provides a simple procedure to generate a class of solvable strongly correlated systems. We illustrate how this procedure works via three physical examples where $N$ particles on a line perform independent (i) Brownian motions, (ii) ballistic motions with random initial velocities, and (iii) Lévy flights, but they get strongly correlated via {\it simultaneous resetting} to the origin. Our results are verified in numerical simulations. This procedure can be used to generate an endless variety of solvable strongly correlated systems. |
| title | Exact extreme, order and sum statistics in a class of strongly correlated system |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2307.15351 |