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pro vyhledávání: '"Melotti, Paul"'
We identify the local limit of massive spanning forests on the complete graph. This generalizes a well-known theorem of Grimmett on the local limit of uniform spanning trees on the complete graph.
Comment: 10 pages, 2 figures
Comment: 10 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2403.11740
Publikováno v:
Discrete Comput Geom (2024)
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle intersection dynamics, (corrugated) pentagram maps and the short diagonal
Externí odkaz:
http://arxiv.org/abs/2208.00244
We prove an explicit expression for the solutions of the discrete Schwarzian octahedron recurrence, also known as the discrete Schwarzian KP equation (dSKP), as the ratio of two partition functions. Each one counts weighted oriented dimer configurati
Externí odkaz:
http://arxiv.org/abs/2208.00239
Publikováno v:
Electron. J. Combin., 29(1), #P1.59, 2022
We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and asymptotic
Externí odkaz:
http://arxiv.org/abs/2003.11006
Publikováno v:
Ann. Inst. Henri Poincar\'e Comb. Phys. Interact., 10(4), 781-817, 2023
Chelkak introduced $s$-embeddings as tilings by tangential quads which provide the right setting to study the Ising model with arbitrary coupling constants on arbitrary planar graphs. We prove the existence and uniqueness of a local transformation fo
Externí odkaz:
http://arxiv.org/abs/2003.08941
Autor:
Melotti, Paul
We study the eight-vertex model at its free-fermion point. We express a new "switching" symmetry of the model in several forms: partition functions, order-disorder variables, couplings, Kasteleyn matrices. This symmetry can be used to relate free-fer
Externí odkaz:
http://arxiv.org/abs/1811.02026
Autor:
Melotti, Paul, Saias, Eric
It is known that the longest simple path in the divisor graph that uses integers $\leq N$ is of length $\asymp N/\log N$. We study the partitions of $\{1,2,\dots, N\}$ into a minimal number of paths of the divisor graph, and we show that in such a pa
Externí odkaz:
http://arxiv.org/abs/1807.07783
Autor:
Melotti, Paul
Publikováno v:
Journal of Combinatorial Theory, Series A. Volume 158, August 2018, Pages 407-448
We study a two-color loop model known as the $C^{(1)}_2$ loop model. We define a free-fermionic regime for this model, and show that under this assumption it can be transformed into a double dimer model. We then compute its free energy on periodic pl
Externí odkaz:
http://arxiv.org/abs/1708.03239
Akademický článek
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If you color a table using k colors, and throw a needle randomly on it, for some proper definition, you get a certain probability that the endpoints will fall on different colors. How can one make this probability maximal? This problem is related to
Externí odkaz:
http://arxiv.org/abs/1501.02441