Abstract:We consider temporal models of rapidly evolving Markovian networks whose edge-formation and dissolution rates are determined by time-dependent spatial kernels. Equivalently, these may be viewed as Markovian networks with $O(1)$ jump rates observed over long time horizons. In this regime, paths of graphon-valued processes obtained by averaging over suitable moving time windows provide natural state descriptors. Under appropriate conditions on the jump-rate kernels, we establish laws of large numbers and large deviation principles for these window-averaged paths, both in the weak topology and in the cut metric. We also show that, without such local averaging, the rapidly oscillating graphon process does not satisfy a nontrivial path-space LDP. The resulting rate functions admit explicit and tractable representations, distinct from those arising in static random graph models and finite-horizon dynamic graph models. We further analyze the associated variational problems in several examples and apply the graphon LDP to node-valent dynamical systems driven by the evolving network.
From: Souvik Ray [view email]
[v1]
Tue, 10 Jun 2025 01:41:25 UTC (61 KB)
[v2]
Sat, 1 Aug 2026 08:02:21 UTC (82 KB)
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