Geometry of the random walk range conditioned on survival among Bernoulli obstacles
We consider a discrete time simple symmetric random walk among Bernoulli obstacles on
Z^ d Z d, d ≥ 2 d≥ 2, where the walk is killed when it hits an obstacle. It is known that …
Z^ d Z d, d ≥ 2 d≥ 2, where the walk is killed when it hits an obstacle. It is known that …
The parabolic Anderson model
W König, T Wolff - Preprint. Available at www. wiasberlin. de/people …, 2015 - Springer
This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …
equation with random potential. This model and many variants and related models are …
Large deviations for Brownian motion in a random potential
D Boivin, TTH Lê - ESAIM: Probability and Statistics, 2020 - esaim-ps.org
A quenched large deviation principle for Brownian motion in a stationary potential is proved.
As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 …
As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 …
Random Walk among Bernoulli Obstacles
C Xu - 2020 - search.proquest.com
The random walk among Bernoulli obstacles model describes a system in which particles
move randomly in a space containing random traps. More precisely, obstacles are placed …
move randomly in a space containing random traps. More precisely, obstacles are placed …
[PDF][PDF] Geometry of the random walk range conditioned on survival among Bernoulli obstacles
福島竜輝 - 数理解析研究所講究録, 2019 - ms.u-tokyo.ac.jp
格子 Zd 上に Bernoulli 分布する障害物を避けながらランダムウォークする粒子を考える.
粒子と媒質の両方について平均をとると (annealed という 2) 粒子は出発点を含む球状の領域に局 …
粒子と媒質の両方について平均をとると (annealed という 2) 粒子は出発点を含む球状の領域に局 …
Details About Intermittency
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
In this chapter, we discuss much stronger and more detailed assertions about intermittency
than we did before. They characterise the long-time behaviour of the mass flow through a …
than we did before. They characterise the long-time behaviour of the mass flow through a …
Some Proof Techniques
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
Abstract In Sect. 3.2, we described the heuristics for the large-t exponential rate of the
moments of the total mass U (t), neglecting all technical issues. More precisely, we only gave …
moments of the total mass U (t), neglecting all technical issues. More precisely, we only gave …
Tools and Concepts
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
One of the most interesting features of the PAM is that, being a partial differential equation
with random coefficients, it lies in the intersection of probability and functional analysis …
with random coefficients, it lies in the intersection of probability and functional analysis …
Almost Sure Asymptotics for the Total Mass
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
In this section, we explain the basic picture that underlies the almost sure asymptotics of the
total mass U (t) under Assumption (H). Like for the moments, we will give an argument only …
total mass U (t) under Assumption (H). Like for the moments, we will give an argument only …
Background, Model and Questions
W König, W König - The Parabolic Anderson Model: Random Walk in …, 2016 - Springer
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