Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Hugo Duminil-Copin"'
Autor:
Hugo Duminil-Copin, Ioan Manolescu
Publikováno v:
Forum of Mathematics, Pi, Vol 10 (2022)
This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in [1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the critical
Externí odkaz:
https://doaj.org/article/6c3c3af98b9941c9aa00ecedcf181799
Autor:
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu, Tatiana Tikhonovskaia
Publikováno v:
Communications in Mathematical Physics
Communications in Mathematical Physics, 2022, 395, pp.1383-1430. ⟨10.1007/s00220-022-04459-x⟩
Communications in Mathematical Physics, 2022, 395, pp.1383-1430. ⟨10.1007/s00220-022-04459-x⟩
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the reg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01032e1ad0639738c313d5cc4d667d11
https://hal.science/hal-03376947
https://hal.science/hal-03376947
Publikováno v:
Probability Theory and Related Fields, 181
Probability Theory and Related Fields
Probability Theory and Related Fields
This paper is studying the critical regime of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4)$. More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f9c841f53b70e6904bc56d9843080b0
https://hdl.handle.net/20.500.11850/492823
https://hdl.handle.net/20.500.11850/492823
Autor:
Marcin Lis, Hugo Duminil-Copin
Publikováno v:
Probability Theory and Related Fields. 175:937-955
We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random curren
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8c04d9cb0cbe12aa9a87a34d283c72d
https://doi.org/10.1007/s00440-019-00899-0
https://doi.org/10.1007/s00440-019-00899-0
Publikováno v:
Inventiones mathematicae. 216:661-743
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This persp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::887ce995d723c5ab443c04bb11418445
https://doi.org/10.1007/s00222-018-00851-4
https://doi.org/10.1007/s00222-018-00851-4
Autor:
Hugo Duminil-Copin
Publikováno v:
Japanese Journal of Mathematics. 14:1-25
This text describes the content of the Takagi Lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for Boolean functions and its application to the study of phase transitions in statistica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9a4c977b91305520a61774c3b2a89317
https://doi.org/10.1007/s11537-018-1726-x
https://doi.org/10.1007/s11537-018-1726-x
Publikováno v:
Annals of Probability
Ann. Probab. 48, no. 5 (2020), 2176-2188
Ann. Probab. 48, no. 5 (2020), 2176-2188
We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ${\mathbb Z}^d$ $(d\geq2)$ in which weights take finitely many values is typically exponentially large.
15 pages, 3 figures
15 pages, 3 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2dcec6a9bdd17d3869eeb5a75b14b783
https://doi.org/10.1214/19-aop1419
https://doi.org/10.1214/19-aop1419
Publikováno v:
Ann. Inst. H. Poincaré Probab. Statist. 56, no. 1 (2020), 391-404
We study internal diffusion-limited aggregation with random starting points on Z^d. In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the aggregate is a Euc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3b5044aadb24cb6eba6ab1a013c69439
https://doi.org/10.1214/19-aihp965
https://doi.org/10.1214/19-aihp965
Autor:
Hugo Duminil-Copin, Michael Aizenman
Publikováno v:
Annals of Mathematics
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$ fields over
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::63a2d5c1d35e4769423ee266abf5719b
https://hal.archives-ouvertes.fr/hal-02440955
https://hal.archives-ouvertes.fr/hal-02440955
Publikováno v:
Communications in Mathematical Physics, 374
Communications in Mathematical Physics
Communications in Mathematical Physics
The truncated two-point function of the ferromagnetic Ising model on Zd (d≥3) in its pure phases is proven to decay exponentially fast throughout the ordered regime (β>βc and h=0). Together with the previously known results, this implies that the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8d9315329e0725c00dc07bec7ba31af
https://hdl.handle.net/20.500.11850/384647
https://hdl.handle.net/20.500.11850/384647