8 papers
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…
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…
Peierls bounds from Toom contours
Jan M. Swart, Réka Szabó, Cristina Toninelli
For deterministic monotone cellular automata on the -dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable aga…
A Course in Interacting Particle Systems
Jan M. Swart
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the m…
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…
Skorokhod's topologies on path space
Nic Freeman, Jan M. Swart
Skorokhod's J1 and M1 topologies are standard tools in proving limit theorems for stochastic processes. Motivated by applications, we extend these topologies so that they are capab…