Alexander Glazman
University of Innsbruck
Ass. Prof. Alexander Glazman, PhD
E-mail: alexander.glazman@uibk.ac.at
Office 728, Technikerstraße 13/7, 6020 InnsbruckPhone: +43 512 507 53930
About me
I am an Assistant Professor at the University of Innsbruck and the PI of the FWF Stand-Alone grant "Order-disorder phase transitions in 2D lattice models".
My field of research lies at the intersection of Probability Theory and Mathematical Physics. Models of statistical mechanics that I am mostly interested in are:
Loop O(n) model, Six-vertex model, Ashkin-Teller model, random-cluster model, Self-Avoiding Walk, Ising model.
Loop O(n) model, Six-vertex model, Ashkin-Teller model, random-cluster model, Self-Avoiding Walk, Ising model.
I did my Ph.D. at the University of Geneva in 2016 under the supervision of Stanislav Smirnov. The title of my PhD thesis is Properties of self-avoiding walks and a stress-energy tensor in the O(n) model. I obtained a degree Candidate of Physico-mathematical sciences and completed my master's degree in St Petersburg at PDMI and SPbU, both under supervision of Dmitry Karpov.
Postdoc job offer
"Postdoc in Probability, University of Innsbruck"
Teaching
- Winter 2022/23: Introduction to Higher Stochastics (Einführung in die Höhere Stochastik)
- Summer 2023: Discrete Probability in models of Mathematical Physics, more information
Papers
- Phase diagram of the Ashkin-Teller model
Available on arXiv
Joint work with Yacine Aoun and Moritz Dober - Structure of Gibbs measures for planar FK-percolation and Potts models
To appear in Probability and Mathematical Physics 2022+
Joint with Ioan Manolescu - Macroscopic loops in the loop \(O(n)\) model via the XOR trick
Available on arXiv
Joint with Nicholas Crawford, Matan Harel, and Ron Peled - On the transition between the disordered and antiferroelectric phases of the \(6\)-vertex model
Available on arXiv
Joint with Ron Peled - Exponential decay in the loop \(O(n)\) model: \(n > 1, x<\tfrac{1}{\sqrt{3}}+\varepsilon(n)\)
In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, (2021), 455-470
Joint with Ioan Manolescu - Uniform Lipschitz functions on the triangular lattice have logarithmic variations
Communications in Mathematical Physics (CMP), vol. 381, 3, (2021), 1153-1221
Joint with Ioan Manolescu - Self-avoiding walk on \(\mathbb{Z}^2\) with Yang-Baxter weights: universality of critical fugacity and 2-point function
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques (AIHP), vol. 56, 4, (2020)
Joint with Ioan Manolescu - Macroscopic loops in the loop O(n) model at Nienhuis' critical point
Journal of the European Mathematical Society (JEMS), vol. 23, 1, (2021), 315--347
Joint with Hugo Duminil-Copin, Ron Peled and Yinon Spinka - Discrete stress-energy tensor in the loop O(n) model
Available on the arXiv
Joint with Dmitry Chelkak and Stanislav Smirnov - On the probability that self-avoiding walk ends at a given point
Annals of Probability (AOP) 44 (2016), no. 2, 955-983
Joint with Hugo Duminil-Copin, Alan Hammond and Ioan Manolescu - Connective constant for a weighted self-avoiding walk on \(\mathbb{Z}^2\)
Electronic Communications in Probability (ECP) 20 (2015), no. 86, 1-13 - Generalized flowers in k-connected graph. Part 2
(Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 417 (2013), Kombinatorika i Teoriya Grafov. VI, 11-85;
translation in J. Math. Sci. (N.Y.) 204 (2015), no. 2, 185–231 - Forms of higher degree over certain fields
(Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 394 (2011), Voprosy Teorii PredstavleniÄ Algebr i Grupp. 22, 209--217, 296;
translation in J. Math. Sci. (N.Y.) 188 (2013), no. 5, 591–595
Joint with Alexander Sivatski, Dmitry Stolyarov and Pavel Zatitsky - Generalized flowers in k-connected graph
(Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 391 (2011), Kombinatorika i Teoriya Grafov. III, 45-78;
translation in J. Math. Sci. (N.Y.) 184 (2012), no. 5, 579–594