Random Walks Across Dimensions: Exploring Simplicial Complexes
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914582981771264 |
|---|---|
| author | Febbe, Diego Fanelli, Duccio Carletti, Timoteo |
| author_facet | Febbe, Diego Fanelli, Duccio Carletti, Timoteo |
| contents | We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order simplices. Optimal search strategies in presence of stochastic teleportation are addressed and the peculiar interplay of noise with higher order structures unraveled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16086 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random Walks Across Dimensions: Exploring Simplicial Complexes Febbe, Diego Fanelli, Duccio Carletti, Timoteo Statistical Mechanics Adaptation and Self-Organizing Systems Physics and Society We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order simplices. Optimal search strategies in presence of stochastic teleportation are addressed and the peculiar interplay of noise with higher order structures unraveled. |
| title | Random Walks Across Dimensions: Exploring Simplicial Complexes |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2601.16086 |