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Conditional-path Monte Carlo for rare stochastic dynamics on networks: Details and derivations — arXiv:2608.17511

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.17511
License (as archived): CC0-1.0
Archived: 2026-10-18T15:56:27.358Z
SHA-256 of the archived text: b024b0e7e3d97e5352e207f6745838b1f95d759d14feff3e55fabbc6c2abd7cc
Stable URL of this page: https://metraipolis.com/documento/dc_008ca69451dc

How to cite

Conditional-path Monte Carlo for rare stochastic dynamics on networks: Details and derivations — arXiv:2608.17511 — arXiv (en), https://arxiv.org/abs/2608.17511 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_008ca69451dc (Metraipolis archive dc_008ca69451dc, sha256 b024b0e7e3d97e5352e207f6745838b1f95d759d14feff3e55fabbc6c2abd7cc)

BibTeX

@misc{dc008ca69451dc,
  title = {Conditional-path Monte Carlo for rare stochastic dynamics on networks: Details and derivations — arXiv:2608.17511},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.17511},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_008ca69451dc; sha256 b024b0e7e3d97e5352e207f6745838b1f95d759d14feff3e55fabbc6c2abd7cc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.17511. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The simulation of rare macroscopic events in stochastic network dynamics, such as widespread epidemic outbreaks, cascading failures in communication networks, or the escape from metastable states in many-body systems, is severely hindered by methodological challenges like catastrophic rejection rates, weight degeneracy, genealogical correlations, and critical slowing down inherent to standard forward-time algorithms, splitting methods, and transition-path sampling. Conditional-path Monte Carlo (CPMC) overcomes these limitations by employing non-local Swendsen-Wang-like cluster updates that operate directly on full-system trajectories. Serving as the technical companion to [Sun, Moody, and Barthel, arXiv:2608.16171 ], this paper provides the rigorous mathematical foundations and algorithmic details underlying the CPMC framework. We formally define the joint path-graph probability weights and derive the transition and uniformization sum rules that guarantee detailed balance. Applying the framework to susceptible-infectious-susceptible (SIS) models, we systematically construct and optimize single-node and edge graph vertex sets specifically designed to prevent lock avalanches and maintain the structural mobility of the epidemic trunk. Furthermore, we detail a dynamic programming scheme to exactly implement complex boundary conditions - including patient-zero and macroscopic outbreak-size constraints - enabling the rejection-free generation of valid trajectories. Finally, we assess the computational complexity of the algorithm, describe parallelization strategies, and validate CPMC against exact solutions for dynamics on small networks.

Tema degli esploratori: governance digitale e beni comuni (retro-catalogo arXiv: annunci del 2026-08-19 in physics.soc-ph).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Social and Information Networks (cs.SI); Computational Physics (physics.comp-ph); Physics and Society (physics.soc-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.17511 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T15:48:19.788Z dalla pagina https://arxiv.org/catchup/physics.soc-ph/2026-08-19?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).