19 citations · 42 across the 6 of their papers we have counts for
7 papers · 1 filter
Semi-open boundary for random walking shocks
Márton Balázs
Non-stationary time evolution of interacting particle systems is in general a rather difficult topic however, exceptional examples are known where hidden processes within the model…
Interacting Particle Systems and Jacobi Style Identities
Márton Balázs, Dan Fretwell, Jessica Jay
We consider the family of nearest neighbour interacting particle systems on allowing , or particles at a site. We parametrize a wide subfamily of processes…
Hydrodynamic limit of the zero range process on a randomly oriented graph
Márton Balázs, Felix Maxey-Hawkins
We prove the hydrodynamic limit of a totally asymmetric zero range process on a torus with two lanes and randomly oriented edges. The asymmetry implies that the model is non-revers…
Local stationarity of exponential last passage percolation
Márton Balázs, Ofer Busani, Timo Seppäläinen
We consider point to point last passage times to every vertex in a neighbourhood of size , distance away from the starting point. The increments of these last…
Large deviations and wandering exponent for random walk in a dynamic beta environment
Márton Balázs, Firas Rassoul-Agha, Timo Seppäläinen
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed env…
Product blocking measures and a particle system proof of the Jacobi triple product
Márton Balázs, Ross Bowen
We review product form blocking measures in the general framework of nearest neighbor asymmetric one dimensional misanthrope processes. This class includes exclusion, zero range, b…
How to initialize a second class particle?
Márton Balázs, Attila László Nagy
We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle sys…