Zobrazeno 1 - 10
of 204
pro vyhledávání: '"Hutchcroft, Tom"'
Let $\Gamma$ be a finitely generated group, and let $\mu$ be a nondegenerate, finitely supported probability measure on $\Gamma$. We show that every co-compact $\Gamma$ action on a locally compact Hausdorff space admits a nonzero $\mu$-stationary Rad
Externí odkaz:
http://arxiv.org/abs/2410.23600
Autor:
Hutchcroft, Tom, Pan, Minghao
We study percolation on nonamenable groups at the uniqueness threshold $p_u$, the critical value that separates the phase in which there are infinitely many infinite clusters from the phase in which there is a unique infinite cluster. The number of i
Externí odkaz:
http://arxiv.org/abs/2409.12283
Autor:
Hutchcroft, Tom
We prove a new inequality bounding the probability that the random walk on a group has small total displacement in terms of the spectral and isoperimetric profiles of the group. This inequality implies that if the random walk on the group is diffusiv
Externí odkaz:
http://arxiv.org/abs/2406.17587
Autor:
Halberstam, Noah, Hutchcroft, Tom
We prove a conjecture of Diaconis and Freedman (Ann. Probab. 1980) characterising the extreme points of the set of partially-exchangeable processes on a countable set. More concretely, we prove that the partially exchangeable sigma-algebra of any tra
Externí odkaz:
http://arxiv.org/abs/2405.20276
Autor:
Hutchcroft, Tom
In long-range percolation on $\mathbb{Z}^d$, we connect each pair of distinct points $x$ and $y$ by an edge independently at random with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta\geq 0$ is a parameter. In a
Externí odkaz:
http://arxiv.org/abs/2404.07276
We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$. We determine the exponent governing the probability to hit a small ball with an exceptio
Externí odkaz:
http://arxiv.org/abs/2312.00711
Autor:
Easo, Philip, Hutchcroft, Tom
We prove Schramm's locality conjecture for Bernoulli bond percolation on transitive graphs: If $(G_n)_{n\geq 1}$ is a sequence of infinite vertex-transitive graphs converging locally to a vertex-transitive graph $G$ and $p_c(G_n) \neq 1$ for every $n
Externí odkaz:
http://arxiv.org/abs/2310.10983
Autor:
Easo, Philip, Hutchcroft, Tom
We prove a quantitative refinement of the statement that groups of polynomial growth are finitely presented. Let $G$ be a group with finite generating set $S$ and let $\operatorname{Gr}(r)$ be the volume of the ball of radius $r$ in the associated Ca
Externí odkaz:
http://arxiv.org/abs/2308.12428
Autor:
Halberstam, Noah, Hutchcroft, Tom
The arboreal gas is the random (unrooted) spanning forest of a graph in which each forest is sampled with probability proportional to $\beta^{\# \text{edges}}$ for some $\beta\geq 0$, which arises as the $q\to 0$ limit of the Fortuin-Kastelyn random
Externí odkaz:
http://arxiv.org/abs/2302.12224
Double-exponential susceptibility growth in Dyson's hierarchical model with $|x-y|^{-2}$ interaction
We study long-range percolation on the $d$-dimensional hierarchical lattice, in which each possible edge $\{x,y\}$ is included independently at random with inclusion probability $1-\exp ( -\beta \|x-y\|^{-d-\alpha} )$, where $\alpha>0$ is fixed and $
Externí odkaz:
http://arxiv.org/abs/2302.01509