Existence of transient two-dimensional random walks on discrete point processes

From papers

A two-dimensional random walk on a discrete point process is a random walk in dimension $2$ whose state space is a discrete point process. Existence conjecture. There are transient two-dimensional random walks on discrete point processes. The paper notes that transience and recurrence are fully classified in dimensions $d=1$ and $d\geq 3$ , but only partially classified in dimension $2$ ; this conjecture asserts that transience can occur there.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Equivalent formulations 1

Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

Existence of transient two-dimensional random walks on discrete point processes
A two-dimensional random walk on a discrete point process is the random walk considered in the paper when the ambient dimension is $2$ . Existence conjecture. There are transient two-dimensional random walks on discrete point processes. The paper states this as an open direction because recurrence and transience are fully classified in dimensions $1$ and at least $3$ , but only partially classified in dimension $2$ .
source: Ron Rosenthal, “Random walk on discrete point processes”, arXiv:1005.1398 (2011).

Sources & referencesView supporting material

Primary source

Noam Berger and Ron Rosenthal, “Behavior of random walk on discrete point processes”, arXiv:1110.5740 (2013).

Additional references

2 papers in this index state this conjecture (2010–2011). The statement above is taken from the most recent of them; the others are arXiv:1005.1398.

1 week ago

No solutions have been posted yet.