%0 Generic %1 bramson2010tightness %A Bramson, Maury %A Zeitouni, Ofer %D 2010 %K Gaussian_free_field branching_random_walk %T Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field %U http://arxiv.org/abs/1009.3443 %X We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long-standing conjecture. The proof combines a recent observation of Bolthausen, Deuschel and Zeitouni with elements from (Bramson 1978) and comparison theorems for Gaussian fields. An essential part of the argument is the precise evaluation, up to an error of order 1, of the expected value of the maximum of the GFF in a box. Related Gaussian fields, such as the GFF on a two-dimensional torus, are also discussed.

@misc{bramson2010tightness, abstract = { We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long-standing conjecture. The proof combines a recent observation of Bolthausen, Deuschel and Zeitouni with elements from (Bramson 1978) and comparison theorems for Gaussian fields. An essential part of the argument is the precise evaluation, up to an error of order 1, of the expected value of the maximum of the GFF in a box. Related Gaussian fields, such as the GFF on a two-dimensional torus, are also discussed. }, added-at = {2011-04-21T22:01:55.000+0200}, author = {Bramson, Maury and Zeitouni, Ofer}, biburl = {https://www.bibsonomy.org/bibtex/27c03c8a33dc9232de42665f5940eeccd/peter.ralph}, description = {[1009.3443] Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field}, interhash = {fb0ff516e5cb97f0be38c5cba446f84f}, intrahash = {7c03c8a33dc9232de42665f5940eeccd}, keywords = {Gaussian_free_field branching_random_walk}, note = {cite arxiv:1009.3443 }, timestamp = {2011-04-21T22:01:55.000+0200}, title = {Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field}, url = {http://arxiv.org/abs/1009.3443}, year = 2010 }