Directed Polymer Transfer Matrices as a Unified Generator of Distinct One-Point Fluctuation Laws
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914395410399232 |
|---|---|
| author | Mu, Sen Saberi, Abbas Ali Moessner, Roderich Kardar, Mehran |
| author_facet | Mu, Sen Saberi, Abbas Ali Moessner, Roderich Kardar, Mehran |
| contents | We revisit the transfer-matrix approach to directed polymers in random media and show that a single ensemble of random transfer-matrix products provides a unified realization of the canonical one-point fluctuation laws in $(1+1)$ dimensions. For a fixed disorder realization, the polymer partition function is obtained as a contraction of the same product matrix $W(t)$, and different contractions reproduce the standard KPZ subclasses: Tracy-Widom GUE (point-to-point), GOE (point-to-line), GSE (half-space point-to-point), and Baik-Rains (stationary line-to-point). In each case, we observe $t^{1/3}$ free-energy fluctuation growth and convergence of standardized distributions with low-order cumulants close to the corresponding universal benchmarks. Viewing geometry-dependent subclasses as projections of a single matrix-product ensemble naturally suggests additional observables intrinsic to $W(t)$. As an example, we examine the leading eigenvalue $λ_1(t)$ whose logarithm exhibits $t^{1/3}$ scaling, while its standardized statistics remain distinct from the canonical Tracy-Widom laws within the accessible range. This transfer-matrix perspective thus organizes known KPZ one-point subclasses within a finite-dimensional matrix framework and highlights matrix-level fluctuation observables beyond geometry-selected universality classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Directed Polymer Transfer Matrices as a Unified Generator of Distinct One-Point Fluctuation Laws Mu, Sen Saberi, Abbas Ali Moessner, Roderich Kardar, Mehran Soft Condensed Matter Disordered Systems and Neural Networks Mathematical Physics Data Analysis, Statistics and Probability We revisit the transfer-matrix approach to directed polymers in random media and show that a single ensemble of random transfer-matrix products provides a unified realization of the canonical one-point fluctuation laws in $(1+1)$ dimensions. For a fixed disorder realization, the polymer partition function is obtained as a contraction of the same product matrix $W(t)$, and different contractions reproduce the standard KPZ subclasses: Tracy-Widom GUE (point-to-point), GOE (point-to-line), GSE (half-space point-to-point), and Baik-Rains (stationary line-to-point). In each case, we observe $t^{1/3}$ free-energy fluctuation growth and convergence of standardized distributions with low-order cumulants close to the corresponding universal benchmarks. Viewing geometry-dependent subclasses as projections of a single matrix-product ensemble naturally suggests additional observables intrinsic to $W(t)$. As an example, we examine the leading eigenvalue $λ_1(t)$ whose logarithm exhibits $t^{1/3}$ scaling, while its standardized statistics remain distinct from the canonical Tracy-Widom laws within the accessible range. This transfer-matrix perspective thus organizes known KPZ one-point subclasses within a finite-dimensional matrix framework and highlights matrix-level fluctuation observables beyond geometry-selected universality classes. |
| title | Directed Polymer Transfer Matrices as a Unified Generator of Distinct One-Point Fluctuation Laws |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2603.14477 |