Negative moments of the CREM partition function in the high temperature regime
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912166797377536 |
|---|---|
| author | Ho, Fu-Hsuan |
| author_facet | Ho, Fu-Hsuan |
| contents | The continuous random energy model (CREM) was introduced by Bovier and Kurkova in 2004 which can be viewed as a generalization of Derrida's generalized random energy model. Among other things, their work indicates that there exists a critical point $β_c$ such that the partition function exhibits a phase transition. The present work focuses on the high temperature regime where $β<β_c$. We show that for all $β<β_c$ and for all $s>0$, the negative $s$ moment of the CREM partition function is comparable with the expectation of the CREM partition function to the power of $-s$, up to constants that are independent of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04329 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Negative moments of the CREM partition function in the high temperature regime Ho, Fu-Hsuan Probability Mathematical Physics 60K35, 60G15, 60J80 The continuous random energy model (CREM) was introduced by Bovier and Kurkova in 2004 which can be viewed as a generalization of Derrida's generalized random energy model. Among other things, their work indicates that there exists a critical point $β_c$ such that the partition function exhibits a phase transition. The present work focuses on the high temperature regime where $β<β_c$. We show that for all $β<β_c$ and for all $s>0$, the negative $s$ moment of the CREM partition function is comparable with the expectation of the CREM partition function to the power of $-s$, up to constants that are independent of $N$. |
| title | Negative moments of the CREM partition function in the high temperature regime |
| topic | Probability Mathematical Physics 60K35, 60G15, 60J80 |
| url | https://arxiv.org/abs/2309.04329 |