[图书][B] Branching random walks
Z Shi - 2015 - Springer
These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …
time branching random walk and to exploit its spinal structure. They begin with the case of …
Critical Liouville measure as a limit of subcritical measures
We study how the Gaussian multiplicative chaos (GMC) measures μ^γ corresponding to the
2D Gaussian free field change when γ approaches the critical parameter 2. In particular, we …
2D Gaussian free field change when γ approaches the critical parameter 2. In particular, we …
First passage sets of the 2D continuum Gaussian free field
J Aru, T Lupu, A Sepúlveda - Probability Theory and Related Fields, 2020 - Springer
We introduce the first passage set (FPS) of constant level-aa of the two-dimensional
continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of …
continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of …
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
W Qian, W Werner - Communications in Mathematical Physics, 2018 - Springer
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary
conditions in a two-dimensional domain with the GFF with zero boundary conditions in the …
conditions in a two-dimensional domain with the GFF with zero boundary conditions in the …
Excursion decomposition of the 2D continuum GFF
J Aru, T Lupu, A Sepúlveda - arXiv preprint arXiv:2304.03150, 2023 - arxiv.org
In this note we show that the 2D continuum Gaussian free field (GFF) admits an excursion
decomposition that is on the one hand similar to the classical excursion decomposition of …
decomposition that is on the one hand similar to the classical excursion decomposition of …
Liouville measure as a multiplicative cascade via level sets of the Gaussian free field
We provide new constructions of the subcritical and critical Gaussian multiplicative chaos
(GMC) measures corresponding to the 2D Gaussian free field (GFF). As a special case we …
(GMC) measures corresponding to the 2D Gaussian free field (GFF). As a special case we …
The largest fragment of a homogeneous fragmentation process
A Kyprianou, F Lane, P Mörters - Journal of Statistical Physics, 2017 - Springer
We show that in homogeneous fragmentation processes the largest fragment at time t has
size e^-t Φ'(p) t^-3 2 (\log Φ)'(p)+ o (1), et Φ′(p¯) t-3 2 (log Φ)′(p¯)+ o (1), where Φ Φ is …
size e^-t Φ'(p) t^-3 2 (\log Φ)'(p)+ o (1), et Φ′(p¯) t-3 2 (log Φ)′(p¯)+ o (1), where Φ Φ is …
Exit sets of the continuum Gaussian free field in two dimensions and related questions
A Sepúlveda - 2017 - research-collection.ethz.ch
The topic of this thesis is the study of geometric properties of the two-dimensional continuum
Gaussian free field (GFF), which is the analogue of Brownian motion when time is replaced …
Gaussian free field (GFF), which is the analogue of Brownian motion when time is replaced …
Scaling limit of critical systems in random geometry
EG Powell - 2017 - repository.cam.ac.uk
This thesis focusses on the properties of, and relationships between, several fundamental
objects arising from critical physical models. In particular, we consider Schramm--Loewner …
objects arising from critical physical models. In particular, we consider Schramm--Loewner …