Geodesic
Annihilating random walks and perfect matchings of planar graphs
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003).

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We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model. 
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     author = {Mattera, Massimiliano},
     title = {Annihilating random walks and perfect matchings of planar graphs},
     journal = {Discrete mathematics & theoretical computer science},
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     doi = {10.46298/dmtcs.3326},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3326/}
}
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Mattera, Massimiliano. Annihilating random walks and perfect matchings of planar graphs. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003). doi : 10.46298/dmtcs.3326. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3326/

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