{"title":"The heat flow, GAF, and SL(2;R)","type":"preprint","external_id":{"arxiv":["2304.06665"]},"publication":"arXiv:2304.06665","_id":"59210","date_updated":"2025-03-31T07:19:14Z","year":"2023","abstract":[{"text":"We establish basic properties of the heat flow on entire holomorphic\nfunctions that have order at most 2. We then look specifically at the action of\nthe heat flow on the Gaussian analytic function (GAF). We show that applying\nthe heat flow to a GAF and then rescaling and multiplying by an exponential of\na quadratic function gives another GAF. It follows that the zeros of the GAF\nare invariant in distribution under the heat flow, up to a simple rescaling.\n  We then show that the zeros of the GAF evolve under the heat flow\napproximately along straight lines, with an error whose distribution is\nindependent of the starting point. Finally, we connect the heat flow on the GAF\nto the metaplectic representation of the double cover of the group\n$SL(2;\\mathbb{R}).$","lang":"eng"}],"user_id":"113768","date_created":"2025-03-31T07:15:53Z","citation":{"ama":"Hall B, Ho C-W, Jalowy J, Kabluchko Z. The heat flow, GAF, and SL(2;R). <i>arXiv:230406665</i>. Published online 2023.","ieee":"B. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “The heat flow, GAF, and SL(2;R),” <i>arXiv:2304.06665</i>. 2023.","mla":"Hall, Brian, et al. “The Heat Flow, GAF, and SL(2;R).” <i>ArXiv:2304.06665</i>, 2023.","chicago":"Hall, Brian, Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “The Heat Flow, GAF, and SL(2;R).” <i>ArXiv:2304.06665</i>, 2023.","apa":"Hall, B., Ho, C.-W., Jalowy, J., &#38; Kabluchko, Z. (2023). The heat flow, GAF, and SL(2;R). In <i>arXiv:2304.06665</i>.","short":"B. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2304.06665 (2023).","bibtex":"@article{Hall_Ho_Jalowy_Kabluchko_2023, title={The heat flow, GAF, and SL(2;R)}, journal={arXiv:2304.06665}, author={Hall, Brian and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }"},"status":"public","author":[{"first_name":"Brian","last_name":"Hall","full_name":"Hall, Brian"},{"first_name":"Ching-Wei","last_name":"Ho","full_name":"Ho, Ching-Wei"},{"full_name":"Jalowy, Jonas","last_name":"Jalowy","first_name":"Jonas"},{"last_name":"Kabluchko","first_name":"Zakhar","full_name":"Kabluchko, Zakhar"}]}