We prove that the Loop O (1) model, a well-known graphical expansion of the Ising model, is
a factor of iid on unimodular random rooted graphs under various conditions, including in …

The random interlacement point process (introduced in [47], generalized in [50]) is a Poisson
point process on the space of labeled doubly infinite nearest neighbour trajectories modulo …

We show that any finitely dependent invariant process on a transitive amenable graph is a
finitary factor of an iid process. With an additional assumption on the geometry of the graph …

It has been shown by van den Berg and Steif (Ann. Probab. 27 (1999) 1501–1522) that the
subcritical and critical Ising model on Z^d is a finitary factor of an iid process (ffiid), whereas …

Abstract A random field X=(X v) v∈ G on a quasi-transitive graph G is a factor of an iid
process if it can be written as X= φ (Y) for some iid process Y=(Y v) v∈ G and equivariant …

A random field $ X=(X_v) _ {v\in G} $ on a quasi-transitive graph $ G $ is a factor of iid if it
can be written as $ X=\varphi (Y) $ for some iid process $ Y=(Y_v) _ {v\in G} $ and …

We develop a method to prove that certain percolation processes on amenable random
rooted graphs are factors of iid (fiid), given that the process is a monotone limit of random …

We show that any finite-entropy, countable-valued finitary factor of an iid process can also
be expressed as a finitary factor of a finite-valued iid process whose entropy is arbitrarily …

In this paper, we study a centered Gaussian field on $\mathbb {Z}^ d $ defined by the
following: the conditional law of the field at any site $ i\in\mathbb {Z}^ d $ is Gaussian of …

For every exponentially ergodic one-dimensional probabilistic cellular automaton with
positive rates, we construct a locally defined coupling-from-the-past flow whose coalescence …