A dimension-wise preferential attachment model for simplicial complexes yields power-law generalized degree distributions for simplices of varying dimension.
Random Walks Across Dimensions: Exploring Simplicial Complexes
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
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.
fields
cond-mat.stat-mech 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
A new random walk operator on simplicial complexes bridges different dimensions hierarchically and uses the walkers' asymptotic distribution to rank the importance of higher-order simplices.
Configuration entropy serves as a reliable proxy for the learned skills of reinforcement learning agents performing tasks in discrete space, validated through walker encounters and chess engine tests.
citing papers explorer
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Model of Simplicial Complexes with dimension-wise preferential attachment
A dimension-wise preferential attachment model for simplicial complexes yields power-law generalized degree distributions for simplices of varying dimension.
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Random Walks Across Dimensions: Exploring Simplicial Complexes
A new random walk operator on simplicial complexes bridges different dimensions hierarchically and uses the walkers' asymptotic distribution to rank the importance of higher-order simplices.
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Smart Walkers in Discrete Space
Configuration entropy serves as a reliable proxy for the learned skills of reinforcement learning agents performing tasks in discrete space, validated through walker encounters and chess engine tests.