Critical Gaussian multiplicative chaos: a review
E Powell - arXiv preprint arXiv:2006.13767, 2020 - arxiv.org
arXiv:2006.13767v3 [math.PR] 2 Jul 2020 Page 1 arXiv:2006.13767v3 [math.PR] 2 Jul 2020
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
Maximum and coupling of the sine-Gordon field
R Bauerschmidt, M Hofstetter - The Annals of Probability, 2022 - projecteuclid.org
For 0< β< 6 π, we prove that the distribution of the centred maximum of the ε-regularised
continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted …
continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted …
Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models
Given a square box $\Lambda_n\subseteq\mathbb Z^ 2$ of side-length $ L^ n $ with $ L, n>
1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\} $ with law …
1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\} $ with law …
Exceptional points of two-dimensional random walks at multiples of the cover time
Y Abe, M Biskup - Probability Theory and Related Fields, 2022 - Springer
We study exceptional sets of the local time of the continuous-time simple random walk in
scaled-up (by N) versions DN⊆ Z 2 of bounded open domains D⊆ R 2. Upon exit from DN …
scaled-up (by N) versions DN⊆ Z 2 of bounded open domains D⊆ R 2. Upon exit from DN …
Multiscale Coupling and the Maximum of Models on the Torus
N Barashkov, TS Gunaratnam, M Hofstetter - … in Mathematical Physics, 2023 - Springer
We establish a coupling between the P (ϕ) 2 measure and the Gaussian free field on the two-
dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on …
dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on …
Critical Brownian multiplicative chaos
A Jego - Probability Theory and Related Fields, 2021 - Springer
Brownian multiplicative chaos measures, introduced in Jego (Ann Probab 48: 1597–1643,
2020), Aïdékon et al.(Ann Probab 48 (4): 1785–1825, 2020) and Bass et al.(Ann Probab 22 …
2020), Aïdékon et al.(Ann Probab 48 (4): 1785–1825, 2020) and Bass et al.(Ann Probab 22 …
A limit law for the maximum of subcritical DG-model on a hierarchical lattice
We study the extremal properties of the" integer-valued Gaussian" aka DG-model on the
hierarchical lattice $\Lambda_n:=\{1,\dots, b\}^ n $(with $ b\ge2 $) of depth $ n $. This is a …
hierarchical lattice $\Lambda_n:=\{1,\dots, b\}^ n $(with $ b\ge2 $) of depth $ n $. This is a …
A limit law for the most favorite point of simplerandom walk on a regular tree
We consider a continuous-time random walk on a regular tree of finite depth and study its
favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped …
favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped …
Near-maxima of the two-dimensional discrete Gaussian free field
Abstract We consider the Discrete Gaussian Free Field (DGFF) in domains DN⊆ Z 2 arising,
via scaling by N, from nice domains D⊆ R 2. We study the statistics of the values order log N …
via scaling by N, from nice domains D⊆ R 2. We study the statistics of the values order log N …
Near-maxima of the two-dimensional Discrete Gaussian Free Field
We consider the Discrete Gaussian Free Field (DGFF) in domains $ D_N\subseteq\mathbb
Z^ 2$ arising, via scaling by $ N $, from nice domains $ D\subseteq\mathbb R^ 2$. We study …
Z^ 2$ arising, via scaling by $ N $, from nice domains $ D\subseteq\mathbb R^ 2$. We study …