Duminil-Copin, Hugo 100 years of the (critical) Ising model on the hypercubic lattice. (English) Zbl 07822674 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 1. Prize lectures. Berlin: European Mathematical Society (EMS). 164-210 (2023). MSC: 82B20 60K35 PDFBibTeX XMLCite \textit{H. Duminil-Copin}, in: International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 1. Prize lectures. Berlin: European Mathematical Society (EMS). 164--210 (2023; Zbl 07822674) Full Text: DOI arXiv OA License
Duminil-Copin, Hugo; Garban, Christophe; Tassion, Vincent Long-range order for critical Book-Ising and Book-percolation. (English) Zbl 07786915 Commun. Math. Phys. 404, No. 3, 1309-1339 (2023). MSC: 82Bxx 60Kxx 82Dxx PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Math. Phys. 404, No. 3, 1309--1339 (2023; Zbl 07786915) Full Text: DOI arXiv OA License
Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; Severo, Franco Equality of critical parameters for percolation of Gaussian free field level sets. (English) Zbl 07684355 Duke Math. J. 172, No. 5, 839-913 (2023). Reviewer: Arnaud Le Ny (Paris) MSC: 60K35 60G60 82B43 60G15 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Duke Math. J. 172, No. 5, 839--913 (2023; Zbl 07684355) Full Text: DOI arXiv
Duminil-Copin, Hugo; Rivera, Alejandro; Rodriguez, Pierre-François; Vanneuville, Hugo Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension \(d\geq 3\). (English) Zbl 1515.60153 Ann. Probab. 51, No. 1, 228-276 (2023); erratum ibid. 52, No. 1, 381-385 (2024). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 60G60 60K35 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Ann. Probab. 51, No. 1, 228--276 (2023; Zbl 1515.60153) Full Text: DOI arXiv
Duminil-Copin, Hugo; Manolescu, Ioan Planar random-cluster model: scaling relations. (English) Zbl 1512.60065 Forum Math. Pi 10, Paper No. e23, 83 p. (2022). Reviewer: Arnaud Le Ny (Paris) MSC: 60K35 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{I. Manolescu}, Forum Math. Pi 10, Paper No. e23, 83 p. (2022; Zbl 1512.60065) Full Text: DOI arXiv
Duminil-Copin, Hugo; Harel, Matan; Laslier, Benoit; Raoufi, Aran; Ray, Gourab Logarithmic variance for the height function of square-ice. (English) Zbl 07613401 Commun. Math. Phys. 396, No. 2, 867-902 (2022). MSC: 82Bxx 60Kxx 05Cxx PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Math. Phys. 396, No. 2, 867--902 (2022; Zbl 07613401) Full Text: DOI arXiv
Duminil-Copin, Hugo; Kozlowski, Karol Kajetan; Krachun, Dmitry; Manolescu, Ioan; Tikhonovskaia, Tatiana On the six-vertex Model’s free energy. (English) Zbl 07606703 Commun. Math. Phys. 395, No. 3, 1383-1430 (2022). MSC: 82Bxx 60Kxx 05Cxx PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Math. Phys. 395, No. 3, 1383--1430 (2022; Zbl 07606703) Full Text: DOI arXiv
Duminil-Copin, Hugo; Manolescu, Ioan; Tassion, Vincent Planar random-cluster model: fractal properties of the critical phase. (English) Zbl 1475.60195 Probab. Theory Relat. Fields 181, No. 1-3, 401-449 (2021). MSC: 60K35 82B43 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Probab. Theory Relat. Fields 181, No. 1--3, 401--449 (2021; Zbl 1475.60195) Full Text: DOI arXiv
Duminil-Copin, Hugo; Kozma, Gady; Tassion, Vincent Upper bounds on the percolation correlation length. (English) Zbl 1469.60325 Vares, Maria Eulália (ed.) et al., In and out of equilibrium 3: celebrating Vladas Sidoravicius. Cham: Birkhäuser. Prog. Probab. 77, 347-369 (2021). MSC: 60K35 82B43 82C43 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Prog. Probab. 77, 347--369 (2021; Zbl 1469.60325) Full Text: DOI arXiv
Aizenman, Michael; Duminil-Copin, Hugo Marginal triviality of the scaling limits of critical 4D Ising and \(\phi_4^4\) models. (English) Zbl 1489.60150 Ann. Math. (2) 194, No. 1, 163-235 (2021); corrigendum ibid. 199, No. 1, 479 (2024). Reviewer: Haru Pinson (Tucson) MSC: 60K35 82B20 82B27 60G60 PDFBibTeX XMLCite \textit{M. Aizenman} and \textit{H. Duminil-Copin}, Ann. Math. (2) 194, No. 1, 163--235 (2021; Zbl 1489.60150) Full Text: DOI arXiv
Duminil-Copin, Hugo; Glazman, Alexander; Peled, Ron; Spinka, Yinon Macroscopic loops in the loop \(O(n)\) model at Nienhuis’ critical point. (English) Zbl 1477.60137 J. Eur. Math. Soc. (JEMS) 23, No. 1, 315-347 (2021). Reviewer: Arnaud Le Ny (Paris) MSC: 60K35 82B20 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., J. Eur. Math. Soc. (JEMS) 23, No. 1, 315--347 (2021; Zbl 1477.60137) Full Text: DOI arXiv
Duminil-Copin, Hugo; Tassion, Vincent Renormalization of crossing probabilities in the planar random-cluster model. (English) Zbl 1482.82034 Mosc. Math. J. 20, No. 4, 711-740 (2020). MSC: 82B43 82B28 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{V. Tassion}, Mosc. Math. J. 20, No. 4, 711--740 (2020; Zbl 1482.82034) Full Text: arXiv Link
Duminil-Copin, Hugo; Goswami, Subhajit; Raoufi, Aran; Severo, Franco; Yadin, Ariel Existence of phase transition for percolation using the Gaussian free field. (English) Zbl 1470.60275 Duke Math. J. 169, No. 18, 3539-3563 (2020). MSC: 60K35 82B43 82B20 05C25 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Duke Math. J. 169, No. 18, 3539--3563 (2020; Zbl 1470.60275) Full Text: DOI arXiv Euclid
Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent Subcritical phase of \(d\)-dimensional Poisson-Boolean percolation and its vacant set. (Phase sous-critique du modèle de percolation Poisson-Booléen et de son complémentaire en dimension \(d\).) (English. French summary) Zbl 1454.82016 Ann. Henri Lebesgue 3, 677-700 (2020). Reviewer: Hasan Akin (Gaziantep) MSC: 82B43 82B26 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Ann. Henri Lebesgue 3, 677--700 (2020; Zbl 1454.82016) Full Text: DOI arXiv
Aizenman, Michael; Duminil-Copin, Hugo; Warzel, Simone Dimerization and Néel order in different quantum spin chains through a shared loop representation. (English) Zbl 1453.82003 Ann. Henri Poincaré 21, No. 8, 2737-2774 (2020). MSC: 82B20 82B43 82B26 82B27 60K35 82D40 PDFBibTeX XMLCite \textit{M. Aizenman} et al., Ann. Henri Poincaré 21, No. 8, 2737--2774 (2020; Zbl 1453.82003) Full Text: DOI arXiv
Duminil-Copin, Hugo Lectures on the Ising and Potts models on the hypercubic lattice. (English) Zbl 1447.82007 Barlow, Martin T. (ed.) et al., Random graphs, phase transitions, and the Gaussian free field. Lecture notes given at the PIMS-CRM summer school in probability, University of British Columbia, Vancouver, Canada, June 5–30, 2017. Cham: Springer. Springer Proc. Math. Stat. 304, 35-161 (2020). MSC: 82B20 82B26 82B43 82B41 60K35 60J67 PDFBibTeX XMLCite \textit{H. Duminil-Copin}, Springer Proc. Math. Stat. 304, 35--161 (2020; Zbl 1447.82007) Full Text: DOI arXiv
Duminil-Copin, Hugo; Goswami, Subhajit; Raoufi, Aran Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature. (English) Zbl 1475.82003 Commun. Math. Phys. 374, No. 2, 891-921 (2020). Reviewer: Farruh Mukhamedov (Kuantan) MSC: 82B20 82B26 82B27 82B43 60K35 82D40 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Math. Phys. 374, No. 2, 891--921 (2020; Zbl 1475.82003) Full Text: DOI arXiv
Duminil-Copin, Hugo; Tassion, Vincent A note on Schramm’s locality conjecture for random-cluster models. (English) Zbl 1446.82006 Sidoravicius, Vladas (ed.), Sojourns in probability theory and statistical physics. II. Brownian web and percolation, a festschrift for Charles M. Newman. Singapore: Springer; Shanghai: NYU Shanghai. Springer Proc. Math. Stat. 299, 123-134 (2019). MSC: 82B20 82B26 82B27 82B43 60K35 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{V. Tassion}, Springer Proc. Math. Stat. 299, 123--134 (2019; Zbl 1446.82006) Full Text: DOI arXiv
Duminil-Copin, Hugo; Lis, Marcin On the double random current nesting field. (English) Zbl 1428.82010 Probab. Theory Relat. Fields 175, No. 3-4, 937-955 (2019). MSC: 82B20 60C05 05C05 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{M. Lis}, Probab. Theory Relat. Fields 175, No. 3--4, 937--955 (2019; Zbl 1428.82010) Full Text: DOI arXiv
Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone Emergent planarity in two-dimensional Ising models with finite-range interactions. (English) Zbl 1417.82022 Invent. Math. 216, No. 3, 661-743 (2019). MSC: 82C20 82C22 82C44 58A17 PDFBibTeX XMLCite \textit{M. Aizenman} et al., Invent. Math. 216, No. 3, 661--743 (2019; Zbl 1417.82022) Full Text: DOI arXiv
Duminil-Copin, Hugo Sharp threshold phenomena in statistical physics. (English) Zbl 1420.82003 Jpn. J. Math. (3) 14, No. 1, 1-25 (2019). Reviewer: Stein Andreas Bethuelsen (Stavanger) MSC: 82B43 82B27 82B26 15B52 PDFBibTeX XMLCite \textit{H. Duminil-Copin}, Jpn. J. Math. (3) 14, No. 1, 1--25 (2019; Zbl 1420.82003) Full Text: DOI arXiv
Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent Exponential decay of connection probabilities for subcritical Voronoi percolation in \(\mathbb{R}^d\). (English) Zbl 1478.60259 Probab. Theory Relat. Fields 173, No. 1-2, 479-490 (2019). MSC: 60K35 82B21 82B43 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Probab. Theory Relat. Fields 173, No. 1--2, 479--490 (2019; Zbl 1478.60259) Full Text: DOI arXiv
Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent Sharp phase transition for the random-cluster and Potts models via decision trees. (English) Zbl 1482.82009 Ann. Math. (2) 189, No. 1, 75-99 (2019). Reviewer: A. C. D. van Enter (Groningen) MSC: 82B20 82B43 60K35 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Ann. Math. (2) 189, No. 1, 75--99 (2019; Zbl 1482.82009) Full Text: DOI arXiv
Duminil-Copin, Hugo Random currents expansion of the Ising model. (English) Zbl 1403.82005 Mehrmann, Volker (ed.) et al., European congress of mathematics. Proceedings of the 7th ECM (7ECM) congress, Berlin, Germany, July 18–22, 2016. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-176-7/hbk; 978-3-03719-676-2/ebook). 869-889 (2018). MSC: 82B20 82D40 82B26 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin}, in: European congress of mathematics. Proceedings of the 7th ECM (7ECM) congress, Berlin, Germany, July 18--22, 2016. Zürich: European Mathematical Society (EMS). 869--889 (2018; Zbl 1403.82005) Full Text: DOI arXiv
Duminil-Copin, Hugo; Li, Jhih-Huang; Manolescu, Ioan Universality for the random-cluster model on isoradial graphs. (English) Zbl 1414.60076 Electron. J. Probab. 23, Paper No. 96, 70 p. (2018). MSC: 60K35 82B20 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Electron. J. Probab. 23, Paper No. 96, 70 p. (2018; Zbl 1414.60076) Full Text: DOI arXiv Euclid
Duminil-Copin, H.; Tassion, Vincent; Teixeira, Augusto The box-crossing property for critical two-dimensional oriented percolation. (English) Zbl 1428.60138 Probab. Theory Relat. Fields 171, No. 3-4, 685-708 (2018). MSC: 60K35 82B43 82C43 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Probab. Theory Relat. Fields 171, No. 3--4, 685--708 (2018; Zbl 1428.60138) Full Text: DOI arXiv
Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent A new computation of the critical point for the planar random-cluster model with \(q\geq1\). (English. French summary) Zbl 1395.82043 Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 1, 422-436 (2018). Reviewer: E. Ahmed (Mansoura) MSC: 82B20 60K35 82B26 82B43 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 1, 422--436 (2018; Zbl 1395.82043) Full Text: DOI arXiv
Duminil-Copin, Hugo; Gagnebin, Maxime; Harel, Matan; Manolescu, Ioan; Tassion, Vincent The Bethe ansatz for the six-vertex and XXZ models: an exposition. (English) Zbl 1430.60080 Probab. Surv. 15, 102-130 (2018). MSC: 60K35 82B20 82B23 82B26 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Probab. Surv. 15, 102--130 (2018; Zbl 1430.60080) Full Text: DOI arXiv Euclid
Duminil-Copin, Hugo; Sidoravicius, Vladas; Tassion, Vincent Continuity of the phase transition for planar random-cluster and Potts models with \({1 \leq q \leq 4}\). (English) Zbl 1357.82011 Commun. Math. Phys. 349, No. 1, 47-107 (2017). MSC: 82B20 60K35 82B26 82D40 82B27 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Math. Phys. 349, No. 1, 47--107 (2017; Zbl 1357.82011) Full Text: DOI arXiv
Beffara, Vincent; Duminil-Copin, Hugo Critical point and duality in planar lattice models. (English) Zbl 1391.82006 Sidoravicius, V. (ed.) et al., Probability and statistical physics in St. Petersburg. St. Petersburg School Probability and Statistical Physics, St. Petersburg State University, St. Petersburg, Russia, June 18–29, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2248-6/hbk; 978-1-4704-2883-9/ebook). Proceedings of Symposia in Pure Mathematics 91, 51-98 (2016). MSC: 82B20 82B27 82B26 82D40 82B43 60K35 PDFBibTeX XMLCite \textit{V. Beffara} and \textit{H. Duminil-Copin}, Proc. Symp. Pure Math. 91, 51--98 (2016; Zbl 1391.82006)
Duminil-Copin, Hugo; Sidoravicius, Vladas; Tassion, Vincent Absence of infinite cluster for critical Bernoulli percolation on slabs. (English) Zbl 1342.82076 Commun. Pure Appl. Math. 69, No. 7, 1397-1411 (2016). MSC: 82B43 60K35 82B26 PDFBibTeX XMLCite \textit{H. Duminil-Copin} et al., Commun. Pure Appl. Math. 69, No. 7, 1397--1411 (2016; Zbl 1342.82076) Full Text: DOI arXiv
Duminil-Copin, Hugo; Tassion, Vincent A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. (English) Zbl 1342.82026 Commun. Math. Phys. 343, No. 2, 725-745 (2016); correction ibid. 359, No. 2, 821-822 (2018). Reviewer: E. Ahmed (Mansoura) MSC: 82B20 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{V. Tassion}, Commun. Math. Phys. 343, No. 2, 725--745 (2016; Zbl 1342.82026) Full Text: DOI arXiv
Duminil-Copin, Hugo; Manolescu, Ioan The phase transitions of the planar random-cluster and Potts models with \(q \geq 1\) are sharp. (English) Zbl 1356.60167 Probab. Theory Relat. Fields 164, No. 3-4, 865-892 (2016). Reviewer: Golibjon Isroilovich Botirov (Bukhara) MSC: 60K35 82B20 82B43 PDFBibTeX XMLCite \textit{H. Duminil-Copin} and \textit{I. Manolescu}, Probab. Theory Relat. Fields 164, No. 3--4, 865--892 (2016; Zbl 1356.60167) Full Text: DOI arXiv
Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas Random currents and continuity of Ising model’s spontaneous magnetization. (English) Zbl 1315.82004 Commun. Math. Phys. 334, No. 2, 719-742 (2015). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B20 82D40 PDFBibTeX XMLCite \textit{M. Aizenman} et al., Commun. Math. Phys. 334, No. 2, 719--742 (2015; Zbl 1315.82004) Full Text: DOI arXiv