39 citations · 180 across the 41 of their papers we have counts for
44 papers · 1 filter
Percolation representations of additive particle systems
Jan M. Swart
It is well-known that additive interacting particle systems with a local state space of cardinality two have a percolation representation in terms of open paths in a graphical repr…
Peierls bounds from random Toom contours
Jan M. Swart, Réka Szabó, Cristina Toninelli
For deterministic monotone cellular automata on the -dimensional integer lattice, Toom (1980) has given necessary and sufficient conditions for the all-one fixed point to be sta…
Tightness criteria for random compact sets of cadlag paths
Nic Freeman, Jan M. Swart
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This…
A min-max random game on a graph that is not a tree
Natalia Cardona-Tobón, Anja Sturm, Jan M. Swart
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a wi…
Universality of the Brownian net
Rongfeng Sun, Jan M. Swart, Jinjiong Yu
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from every point in space and time, while the Brownian net is an extension that also allows…
Monotone duality of interacting particle systems
Jan Niklas Latz, Jan M. Swart
The duality theory for monotone interacting particle systems was initiated by Gray (1986) and further developed by Sturm and Swart (2018). It contains the better known additive dua…