Projects per year
Personal profile
Research interests
Please see my personal webpage for information on my research.
Available PhD projects
Various phenomena in last passage percolation
Place i.i.d. random weights on the vertices of the planar lattice Z^2, and consider two points in that lattice. The first passage percolation (FPP) problem asks about the paths on Z^2 between these two points that collect the least total weight along the way. Questions include existence, uniqueness, and geometric properties (e.g., fluctuations from the straight line between the two points) of such paths, as well as asymptotics (Law of Large Numbers, fluctuations) of the total weight collected by them. While this model is very natural, even some of the most basic questions seem very hard.
The last passage percolation problem asks the same questions, but for the paths collecting the largest total weight along the way. To make sense of this, one restricts the relative position of the two points to NorthEast, as well as the possible steps of the paths to either North or East on the lattice. Suddenly more structure is available and many more questions have been answered than in FPP. There are still things to explore, this is what this topic will be about. We'll use probabilistic arguments, admiration for those will be useful.
Fluctuations in interacting particle systems
In this field particles are placed on the sites of the integer line Z, and a stochastic dynamics is run on the resulting configurations. The main feature, which makes these models both interesting and difficult at the same time, is that the particles influence each other, hence the word "interacting" in the title. Under rather general assumptions the models exhibit nonconventional scaling properties: rather than squareroot scaling and Normal distributional limits, one often finds onethird power of scaling and other limit distributions. This has been proved for a handful of models and not yet proved for many others in the area. This project will concentrate on using probabilistic arguments to prove sharper and/or more general results than available on such exotic scalings.
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Collaborations and top research areas from the last five years

Particle systems, growth models and their probabilistic structures
5/12/22 → 4/12/25
Project: Research

Stochastic interacting systems: connections, fluctuations and applications
1/06/18 → 20/05/22
Project: Research
Research output
 31 Article (Academic Journal)

Hydrodynamic limit of the zero range process on a randomly oriented graph
Balazs, M. & MaxeyHawkins, F. M., 11 Feb 2022, (Epub ahead of print) In: Electronic Journal of Probability. 27, 29 p., 23.Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open AccessFile10 Downloads (Pure) 
Interacting Particle Systems and Jacobi style identities
Balazs, M., Jay, J. & Fretwell, D., 21 Jul 2022, In: Research in the Mathematical Sciences. 9, 3, 39 p., 48.Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open AccessFile7 Downloads (Pure) 
Local stationarity in exponential lastpassage percolation
Balazs, M., Busani, O. & Seppalainen, T., 15 Mar 2021, In: Probability Theory and Related Fields. 180, 12, p. 113162 50 p.Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open Access3 Citations (Scopus)
Activities
 2 Visiting an external academic institution

Alfred Renyi Institute of Mathematics
Marton Balazs (Visitor)
1 Feb 2013 → 31 Aug 2013Activity: Visiting an external institution types › Visiting an external academic institution

Budapest University of Technology and Economics
Marton Balazs (Visiting researcher)
1 Sept 2006 → 31 Aug 2013Activity: Visiting an external institution types › Visiting an external academic institution