The 3D Brownian intersection exponents are analytic: λ ↦ ξ_3(k,λ) is real analytic on (0,∞) for all k≥1, proved via a new boundary Harnack principle for Brownian slit domains.
Intersection exponents for biased random walks on discrete cylinders
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove existence of intersection exponents xi(k,lambda) for biased random walks on d-dimensional half-infinite discrete cylinders, and show that, as functions of lambda, these exponents are real analytic. As part of the argument, we prove convergence to stationarity of a time-inhomogeneous Markov chain on half-infinite random paths. Furthermore, we show this convergence takes place at exponential rate, an estimate obtained via a coupling of weighted half-infinite paths.
fields
math.PR 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents
The 3D Brownian intersection exponents are analytic: λ ↦ ξ_3(k,λ) is real analytic on (0,∞) for all k≥1, proved via a new boundary Harnack principle for Brownian slit domains.