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Subsequential tightness of the maximum of two dimensional Ginzburg-Landau fields. (English) Zbl 07055623
Summary: We prove the subsequential tightness of centered maxima of two-dimensional Ginzburg-Landau fields with bounded elliptic contrast.

60G60 Random fields
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[1] D. Belius and W. Wu, Maximum of the Ginzburg-Landau fields, arXiv preprint arXiv:1610.04195 (2016).
[2] M. Biskup and O. Louidor, Extreme local extrema of two-dimensional discrete Gaussian free field, Comm. Math. Phys. 345 (2016), no. 1, 271-304. · Zbl 1347.82007
[3] E. Bolthausen, J.-D. Deuschel, and O. Zeitouni, Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field, Electron. Commun. Probab. 16 (2011), 114-119. · Zbl 1236.60039
[4] M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc. 44 (1983), no. 285, iv+190. · Zbl 0517.60083
[5] M. Bramson, J. Ding, and O. Zeitouni, Convergence in law of the maximum of the two-dimensional discrete Gaussian free field, Comm. Pure Appl. Math. 69 (2016), no. 1, 62-123. · Zbl 1355.60046
[6] H. J. Brascamp and E. H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, Journal of Functional Analysis 22 (1976), no. 4, 366-389. · Zbl 0334.26009
[7] F. M. Dekking and B. Host, Limit distributions for minimal displacement of branching random walks, Probab. Theory Related Fields 90 (1991), no. 3, 403-426. · Zbl 0734.60074
[8] J. Ding, R. Roy, and O. Zeitouni, Convergence of the centered maximum of log-correlated Gaussian fields, Annals Probab. 45 (2017), 3886-3928. · Zbl 1412.60058
[9] T. Funaki and H. Spohn, Motion by mean curvature from the Ginzburg-Landau interface model, Comm. Math. Phys. 185 (1997), no. 1, 1-36. · Zbl 0884.58098
[10] B. Helffer and J. Sjöstrand, On the correlation for Kac-like models in the convex case, Journal of Statistical Physics 74 (1994), no. 1-2, 349-409. · Zbl 0946.35508
[11] G. F. Lawler, Intersections of random walks, Birkhauser, 1996. · Zbl 0925.60078
[12] J. Miller, Fluctuations for the Ginzburg-Landau \(\nabla \phi\) interface model on a bounded domain, Comm. Math. Phys. 308 (2011), no. 3, 591-639. · Zbl 1237.82030
[13] A. Naddaf and T. Spencer, On homogenization and scaling limit of some gradient perturbations of a massless free field, Comm. Math. Phys. 183 (1997), no. 1, 55-84. · Zbl 0871.35010
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