Link to my MathSciNet publication list: CLICK HERE

Link to my Google Scholar publication list: CLICK HERE

Lecture notes:

• Alexander Drewitz, Balazs Rath, Artem Sapozhnikov:
  An Introduction to Random Interlacements
  SpringerBriefs in Mathematics, 2014. preliminary version, final version.

Papers in pure mathematics:

• Yijie Bi, Zhenhao Cai, Xinyi Li, Balázs Ráth, Yuan Zhang:
  Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
  (submitted) arXived version
  

• Joanna Jasinska, Balázs Ráth:
  Permuton limit of a generalization of the Mallows and k-card-minimum models
  Electronic Communications in Probability, 2025, Vol. 30, paper no. 19, 1-12. ECP version
  

• Balázs Ráth, Márton Szõke, Lutz Warnke:
  Local limit of the random degree constrained process
  (submitted) arXived version
  

• Dániel Keliger, Balázs Ráth:
  Concentration and mean field approximation results for Markov processes on large networks
  (submitted) arXived version
  

• Márton Borbényi, Balázs Ráth, Sándor Rokob:
  Random interlacement is a factor of i.i.d.
  Electronic Journal of Probability 28: 1-45 (2023). EJP version
  

• Balázs Ráth, Kitti Varga, Panna Tímea Fekete, Roland Molontay:
  Color-avoiding percolation and branching processes
  Journal of Applied Probability Volume 61, Issue 3, September 2024, pp. 942 - 966 long arXived version with different title , shortened version , published version ,
  

• Balazs Rath, Sandor Rokob:
  Percolation of worms
  Stochastic Processes and their Applications 2022, Vol. 152, October 2022, pp 233-288. journal webpage of paper , arXived version
  

• Balazs Rath, Jan Swart, Marton Szoke:
  A phase transition between endogeny and nonendogeny
  Electronic Journal of Probability 27: 1-43 (2022). DOI: 10.1214/22-EJP872 EJP version
  

• Balazs Rath, Daniel Valesin:
  On the threshold of spread-out contact process percolation
  Ann. Inst. H. Poincaré Probab. Statist. 58(3): 1808-1848 (August 2022). DOI: 10.1214/21-AIHP1214 journal webpage of paper , arXived version
  

• Balazs Rath, Jan Swart, Tamas Terpai:
  Frozen percolation on the binary tree is nonendogenous
  Annals of Probability 2021, Vol. 49 (5) 2272 - 2316. PDF , journal webpage of paper
  

• Edward Crane, Balazs Rath, Dominic Yeo:
  Age evolution in the mean field forest fire model via multitype branching processes
  Annals of Probability 2021, Vol. 49, No. 4, 2031-2075. PDF , journal webpage of paper
  

• Balazs Rath:
  A moment-generating formula for Erdos-Renyi component sizes.
  Electronic Communications in Probability 2018, Vol. 23, paper no. 24, 1-14. ECP version
  

• Balazs Rath, Daniel Valesin:
  On the threshold of spread-out voter model percolation.
  Electron. Commun. Probab. Volume 22 (2017), paper no. 50, 12 pp. ECP version
  

• James Martin, Balazs Rath:
  Rigid representations of the multiplicative coalescent with linear deletion.
  Electron. J. Probab. Volume 22 (2017), paper no. 83, 47 pp. EJP version
  

• Balazs Rath:
  Feller property of the multiplicative coalescent with linear deletion.
  Bernoulli, Vol. 25, No. 1, 221-240. (2019) Published version
  

• Balazs Rath, Daniel Valesin:
  Percolation on the stationary distributions of the voter model.
  Ann. Probab. Volume 45, Number 3 (2017), 1899-1951. arXived version
  

• Balazs Rath:
  A short proof of the phase transition for the vacant set of random interlacements.
  Electron. Comm. Probab. 20 (3), 1-11, (2015) ECP version
  

• Serguei Popov, Balazs Rath:
  On decoupling inequalities and percolation of excursion sets of the Gaussian free field
  J. of Stat. Phys., April 2015, Volume 159, Issue 2, pp 312-320 arXived version
  

• Alexander Drewitz, Balazs Rath, Artem Sapozhnikov:
  On chemical distances and shape theorems in percolation models with long-range correlations
  Journal of Mathematical Physics 55, 083307, 2014 arXived version
  

• Alexander Drewitz, Balazs Rath, Artem Sapozhnikov:
  Local percolative properties of the vacant set of random interlacements with small intensity
  Annales de l'Institut Henri Poincare, Vol. 50, No. 4, 1165–1197, 2014. arXived version
  

• Balazs Rath, Artem Sapozhnikov:
  The effect of small quenched noise on connectivity properties of random interlacements
  Electronic Journal of Probability, vol. 18, no. 4, Pages 1-20. EJP version
  

• Carlos Hoppen, Yoshiharu Kohayakawa, Carlos Gustavo Moreira, Balazs Rath, Rudini Menezes Sampaio:
  Limits of permutation sequences
  Journal of Combinatorial Theory, Series B, Volume 103, Issue 1, Pages 93-113, 2013. arXived version
  

• Balazs Rath, Artem Sapozhnikov:
  On the transience of random interlacements
  Electronic Communications in Probability , 16: 379-391, 2011. arXived version
  

• Balazs Rath, Artem Sapozhnikov:
  Connectivity properties of random interlacement and intersection of random walks
  ALEA Latin American Journal of Probability and Mathematical Statistics , 9, 67-83, 2012. arXived version
  

• Balazs Rath, Laszlo Szakacs:
  Multigraph limit of the dense configuration model and the preferential attachment graph
  Acta Math. Hun. vol. 136, no. 3, pp. 196-221, 2012. arXived version
  

• Balazs Rath:
  Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics
  Random Structures and Algorithms vol 41(3), 365-390, 2012. arXived version
  

• Istvan Kolossvary and Balazs Rath:
  Multigraph limits and exchangeability
  Acta Math. Hun. vol. 130, no. 1-2, pp. 1-34, 2011. arXived version
  

• Balazs Rath:
  Mean field frozen percolation
  Journal of Statistical Physics vol. 137, no. 3, pp. 459-499, 2009. arXived version
  

• Balazs Rath and Balint Toth:
  Erdos-Renyi Random graphs + forest fires = Self-Organized Criticality
  Electronic Journal of Probability 14:1290-1327, 2009 EJP version
  

• Balint Felszeghy, Balazs Rath and Lajos Ronyai:
  The lex game and some applications
  J. Symbolic Computation 41:663-681, 2006. pdf
  

Papers in applied mathematics and non-rigorous papers:

• Xiangyi Meng, Bingjie Hao, Balázs Ráth, István A. Kovács:
  Path Percolation in Quantum Communication Networks
  Phys. Rev. Lett. 134, 030803, 2025, journal link , arXived version
  

• Ivan Bonamassa, Balázs Ráth, Márton Pósfai, Miklós Abért, Dániel Keliger, Balázs Szegedy, János Kertész, László Lovász, Albert-László Barabási:
  Logarithmic kinetics and bundling in random packings of elongated 3D physical links
  Proceedings of the National Academy of Sciences 2025, DOI number 10.1073/pnas.2427145122 published version , arXived version
  

• Vladas Sidoravicius, Balazs Rath:
  One-dimensional Multi-particle DLA -- a PDE approach
  (withdrawn), 2017, arXived version
  

• Katherine A. Bold, Karthikeyan Rajendran, Balazs Rath, Ioannis G. Kevrekidis:
  An equation-free approach to coarse-graining the dynamics of networks
  Journal of Computational Dynamics 1.1 (2014): 111-134 arXived version
  

• Balazs Gerencser, Balazs Rath, Gabor Tusnady:
  Multifactorial inheritance with selection
  Acta Math. Hun. DOI: 10.1007/s10474-012-0248-x, 2012. link
  

• Balazs Rath and Balint Toth:
  Triangle percolation in mean field random graphs -- with PDE
  Journal of Statistical Physics vol. 131, no. 3, pp. 385-391, 2008. arXived version
  

MSc, PhD theses:

• Balazs Rath:
  Conformal invariance of critical percolation on the triangular lattice
  (MSc thesis, supervisor: Balint Toth) 2005. pdf
  

• Balazs Rath:
  Asymptotic behavior of random graphs evolving in time
  (PhD thesis, supervisor: Balint Toth) 2010. pdf (forest fire + frozen percolation + edge reconnecting model, with many sketch proofs)