2 results
On some threshold-one attractive interacting particle systems on homogeneous trees
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 57 / Issue 3 / September 2020
- Published online by Cambridge University Press:
- 04 September 2020, pp. 866-898
- Print publication:
- September 2020
-
- Article
- Export citation
-
We consider the threshold-one contact process, the threshold-one voter model and the threshold-one voter model with positive spontaneous death on homogeneous trees
$\mathbb{T}_d$
, 
$d\ge 2$
. Mainly inspired by the corresponding arguments for the contact process, we prove that the complete convergence theorem holds for these three systems under strong survival. When the system survives weakly, complete convergence may also hold under certain transition and/or initial conditions.
Lp–Lrestimates for the Poisson semigroup on homogeneous trees
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 64 / Issue 1 / February 1998
- Published online by Cambridge University Press:
- 09 April 2009, pp. 20-32
- Print publication:
- February 1998
-
- Article
-
- You have access
- Export citation
-
Let
be a homogeneous tree of degree at least three. In this paper we investigate for which values of p and r the (σθ)-Poisson semigroup is Lp – Lr,-bounded, and we sharp estimate for the corresponding operator norms.
be a homogeneous tree of degree at least three. In this paper we investigate for which values of 