Julia Komjathy
Delft University of Technology 
This picture is about 10 years old now..., about to be replaced.

Research interests
News, upcoming talks
I am organising the probability and statistics seminar, here is our current list of speakers:
Seminar Series in Probability and Statistics at TU Delft
I will be one of the keynote speakers at WAW 2024, 37 June in Warsaw
``WAW 2024: 19th Workshop on Modelling and Mining Networks''
I will speak at the Discrete Probability Days, Barcelona 1620 Oct 2023
Discrete Probability Days at CRM
Phd students, postdocs
Thesis: Universality of weighted scalefree configuration model
jointly with Remco van der Hofstad, award date: 6 Feb 2017
[ link to Enrico's thesis at Tue library ]
Thesis: Random intersection graphs
jointly with Remco van der Hofstad, award date: June 16 2020
[ link to Viktoria's thesis at Tue library ]
Viktoria is a TT at University of Miskolc, Hungary [ link to Viktoria's website ]
Thesis: Reliable geometric spanners
jointly with Kevin Buchin, award date: 10 July 2021
[ link to Daniel's thesis at Tue library ]
Thesis: Distances and components in scalefree random graph models
graduated on 18 April 2023
[ link to Joost's website ]
[ link to Joost's thesis at Tue library ]
postdoc. Topic: Contact processes and kcores.
Zsolt is currently at the Renyi institute in Budapest.
My latest preprints and papers

Z. Bartha, J. Komjathy, D.Valesin
Degreedependent contact processes
[ arXiv ]
Short description: The degreedependent contact process is an interacting particle system. Infected particles heal at rate one, and while infected, they infect their neighbors in an underlying graph. The infection rate through each edge depends now on the degree of the sender and the receiver vertex, so that the rate lambda is slowed down to and from high degree vertices, by a polynomial of the maximum of these two degrees. We then run this process on GaltonWatson trees and the configuration model and discover new phase transitions compared to the classical contact process. We show that as the exponent of the polynomial increases, on Galton Watson trees global survival but local extinction may happen for arbitrarily small lambda, and also extinction can happen on powerlaw Galton Watson trees, depending on the exact last moment finite of the offspring distribution. In the survival regime, since the surroundings of high degree vertices (stars) heal quickly, we find new structures that sustain the infection for an exponentially long time on the configuration model: kcores.

J. Komjathy, J. Lapinskas, J.Lengler, U. Schaller
Four universal growth regimes in degreedependent first passage percolation on spatial random graphs I
[ arXiv ]
Short description: Onedependent first passage percolation is a spreading process on a graph where the transmission time through each edge depends on the direct surroundings of the edge. In particular, the classical iid transmission time is multiplied by a polynomial of the expected degrees of the endpoints of the edge, which we call the penalty function. We then run this process on three spatial scalefree random graph models. We show that as the penalty increases, the transmission time between two far away vertices sweeps through four universal phases: explosive (with tight transmission times), polylogarithmic, polynomial but strictly sublinear, and linear in the Euclidean distance. The strictly polynomial growth phase here is a new phenomenon that so far was extremely rare in spatial graph models. The four growth phases are highly robust in the model parameters and are not restricted to phase boundaries. In this paper we develop new methods to prove the upper bounds in all subexplosive phases.

J. Komjathy, J. Lapinskas, J.Lengler, U. Schaller
Four universal growth regimes in degreedependent first passage percolation on spatial random graphs II
[ arXiv ]
Short description: In this paper we develop new methods to prove the lower bounds in the above paper, when the growth of the first passage percolation is either polynomial or linear.

J. Jorritsma, J. Komjathy, D. Mitsche
Clustersize decay in supercritical kernelbased spatial random graphs
[ arXiv ]
Short description: The starting point is a classical result of percolation from the 1980s: in Bernoulli percolation on the integer lattice in d dimensions, the probability that the cluster of the origin is at least k but not infinite decays stretched exponentially in k, and the stretch exponent is (d1)/d, where d is the dimension of the model. This has a physical interpretation that is related to surface tension. We look at the same problem on spatial random graphs in more generality, where the models we consider also contain longrange edges and `superspreaders' (hubs). We identify when and how this structural inhomogeneity deforms the surfacetension driven clusters: they are spreadout in space, governed either by longrange edges or by superpreaders, or both, which implies that the stretchexponent changes to four possible values, which constitutes a phase diagram for cluster sizedecay. The stretchexponents also give information on the topology inside the giant component, and govern the speed of lowerlarge deviations for the size of the giant.

J. Jorritsma, J. Komjathy, D. Mitsche
Clustersize decay in supercritical longrange percolation
[ arXiv ]
Short description:In this paper we study cluster sizes in longrange percolation in dimension d which is at least 2. The probability that the cluster of the origin is at least k but not infinite decays stretched exponentially in k, and the stretch exponent is conjectured to be the minimum of (d1)/d, and 2alpha, where alpha governs the longrange connection probability. In this paper we prove this result when the minimum is (d1)/d, which gives the part of the phase diagram that was left open in the paper "Clustersize decay in supercritical kernelbased spatial random graphs" above.

G. Odor, D. Czifra, J. Komjathy, L. Lovasz, and M. Karsai
Switchover phenomenon induced by epidemic seeding on geometric networks
Proceedings of the National Academy of Sciences,
(PNAS), Vol 118 (41) 118 (41) e2112607118 (2021)
[ journal, open access ] [ arXiv ]
Short description: This Covidinspired paper investigates the effect of the initial seeding of an epidemic on the final outbreak size. Starting an epidemic from the bestconnected nodes of a network would intuitively lead to the largest outbreak. We challenge this picture and show that: Epidemics started from the central part of a geometric metapopulation network can reach more individuals only if the basic reproduction number is small, but if the epidemic is more infectious, it reaches a larger population when seeded from uniformly selected nodes. We show that spatial geometry amplifies this effect in both datadriven and synthetic epidemic models, and we give mathematical proofs that this phenomenon appears in various random graph models. These results help us understand why real epidemics started from seemingly similar conditions may have significantly different outcomes.

J. Jorritsma, and J. Komjathy
Distance evolutions in growing preferential attachment graphs (2022)
Annals of Applied Probability, 32(6): 43564397 (Dec 2022).
[ journal ] [ arXiv ]
Short description: This paper is the first to study how graph (and weighted) distances in preferential attachmenttype models shrink as the graph grows around two vertices chosen uniformly at random at some time t. It shows that the graphdistance stays in a tight strip around the main order term for all later times, and eventually settles on 2.
up to date on 14 April 2022

Z. Bartha, J. Komjathy, J. Raes
Sharp bound on the threshold metric dimension of trees
Discrete Mathematics
Vol 346 (8) 113410 (Aug 2023)
[ journal, open access ] [ arXiv ]

J. Jorritsma, and J. Komjathy
Distance evolutions in growing preferential attachment graphs (2022)
Annals of Applied Probability, 32(6): 43564397 (Dec 2022)
[ journal ] [ arXiv ]

R. van der Hofstad, J. Komjathy and V. Vadon
Phase transition in random intersection graphs with communities (2022)
Random Structured and Algorithms Vol. 60, Issue 3, 406461 (2022)
[ journal ] [ arXiv ]

G. Odor, D. Czifra, J. Komjathy, L. Lovasz, and M. Karsai
Longerterm seeding effects on epidemic processes: a network approach
Scientia et Securitas Vol 2, Issue 4, p 409417 (2022)
[ journal, open access ]

G. Odor, D. Czifra, J. Komjathy, L. Lovasz, and M. Karsai
Switchover phenomenon induced by epidemic seeding on geometric networks
Proceedings of the National Academy of Sciences,
(PNAS), Vol 118 (41) 118 (41) e2112607118 (2021)
[ journal ] [ arXiv ]

L. A. Goldberg, J. Jorritsma, J. Komjathy, and J. Lapinskas
Increasing efficacy of contacttracing applications by user referrals and stricter quarantining (2021)
PLoS One, 16 (5): e0250435 (2021)
[ journal ] [ medRXiv ]

R. van der Hofstad, J. Komjathy and V. Vadon
Random Intersection Graphs with Communities
Advances in Applied Probability online first (Nov 2021)
[ journal ] [ arXiv ]

J. Komjathy, J. Lapinskas and J. Lengler
Stopping explosion by penalising transmission to hubs in scalefree spatial random graphs (2021)
Annales de l'Institute Henri Poincare, Vol. 57 (4) p:19682016, (Nov 2021)
[ journal ] [ arXiv ]

J. Komjathy, and G. Odor
The metric dimension of critical GaltonWatson trees and linear preferential attachment trees (2021)
European Journal of Combinatorics Vol 95, pages 103317, (June 2021)
[ journal ] [ arXiv ]

J. Jorritsma, T. Hulshof and J. Komjathy
Not all interventions are equal for the height of the second peak (2020)
Chaos, Solitons \& Fractals Vol. 139: 109965 (2020)
[ journal ] [ arXiv ]

J. Jorritsma, and J. Komjathy
Weighted distances in scalefree preferential attachment models (2020)
Random Structures and Algorithms, Vol 57 (3): 823859 (2020)
[ journal ] [ arXiv ]

J. Komjathy and B. Lodewijks
Explosion in weighted Hyperbolic Random Graphs and Geometric Inhomogeneous Random Graphs (2020)
Stochastic Processes and their Applications Vol. 130(3), pages 13091367 (2020)
[ journal ] [ arXiv ]

V. Vadon, J. Komjathy and R. van der Hofstad
A new model for overlapping communities with arbitrary internal structure
Applied Network Science, Vol 4:42 (2019)
[ journal ]

J. Komjathy, R. Molontay and K. Simon
Transfinite fractal dimension of trees and hierarchical scalefree graphs
Journal of Complex Networks, cnz005 (2019)
[ journal ] [ arXiv ]

E. Baroni and R. van der Hofstad and J. Komjathy
Tight fluctuations of weightdistances in random graphs with infinitevariance degrees
Journal of Statistical Physics Vol 174, Issue 4, pp 906  934 (2019)
[ journal ] [ arXiv ]

E. Adriaans and J. Komjathy
Weighted distances in scale free configuration models
Journal of Statistical Physics Vol 173 (3) p: 1082  1109 (2018)
[ journal ] [ arXiv ]

R. van der Hofstad and J. Komjathy
Explosion and distances in scalefree percolation (2017 June)
[ arXiv ]

K. Simon, S. Molnar, J. Komjathy, P. Mora
Large Deviation Multifractal Analysis of a Process Modeling TCP CUBIC (2017 June)
[ arXiv ]

R. van der Hofstad and J. Komjathy
When is a scalefree graph ultrasmall?
Journal of Statistical Physics Vol. 169 (2), pp 223  264, (2017).
[ journal ] [ arxiv ]

E. Baroni and R. van der Hofstad and J. Komjathy
Nonuniversality of weighted random graphs with infinite variance degrees
Journal of Applied Probability Vol 54, Issue 1 p. 146  164 (2017)
[ arXiv ] [ journal ]

J. Komjathy
Explosion of CrumpModeJagers branching processes (2016 Feb)
[ arXiv ]

J. Komjathy and V. Vadon
First passage percolation on the NewmanWatts small world model
Journal of Statistical Physics, vol. 162, Issue 4, p. 959993 (2016)
[ arXiv ] [ journal ]

J. Komjathy:
Fixed speed competition on the configuration model with infinite variance degrees: equal speeds (2015 Mar)
[ arXiv ]

E. Baroni and R. v. d. Hofstad and J. Komjathy:
Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds
Electronic Journal of Probability, vol 20. no. 116, p. 148 (2015)
[ arXiv] [ journal ]

S. Bhamidi and R. v. d. Hofstad and J. Komjathy:
The front of the epidemic curve and first passage percolation,
Journal of Applied Probability, vol. 51A p. 101121 2014.
[ arXiv ] [ journal ]

I. Kolossvary and J. Komjathy and L. Vago:
Degrees and distances in random and evolving Apollonian networks
Advances in Applied Probability, vol. 48, no. 3 p. 865902. 2016.
[ arXiv ] [ journal ]

S. Bhamidi and J. Goodman and R. v. d. Hofstad and J. Komjathy:
Degree distribution of shortest path trees and bias of network sampling algorithms,
Annals of Applied Probability vol. 25, no. 4, p. 17801826. (2015)
[ arXiv ] [ journal ]

J. Komjathy and Y. Peres:
Topics in Markov chains: Mixing and escape rate
Proceedings of Symposia in Pure Mathematics, Volume 91, (2016)
(Probability and Statistical Physics in St. Petersburg)
[ arXiv ] [ journal ]

I. Kolossvary and J. Komjathy:
First passage percolation on inhomogeneous random graphs,
Advances of Applied Probability vol 47 No. 2 p. 589610. (2015)
[ arXiv ] [ journal ]

J. Komjathy and Y. Peres:
Mixing and relaxation time for random walk on wreath product graphs,
Electronic Journal of Probability, vol. 18, 71, p. 123, (2013)
[ arXiv ] [ journal ]

J. Komjathy and J. Miller and Y. Peres:
Uniform mixing time for random walk on lamplighter graphs,
Annales de l'Institute Henri Poincare, vol. 50, (Number 4) p. 11401160 (2014)
[ arXiv ] [ journal ]

J. Komjathy and K. Simon:
Generating hierarchical scale free graphs from fractals,
Chaos, Solitons and Fractals, vol. 44, p. 651666, (2011)
[ arXiv ] [ journal ]

M. Balazs and J. Komjathy and T. Seppalainen:
Fluctuation bounds in the exponential bricklayers process,
Journal of Statistical Physics, vol. 147, no. 1, p. 3562, 2012
[ journal ]

M. Balazs and J. Komjathy and T. Seppalainen:
Microscopic concavity and fluctuation bounds in a class of deposition processes,
Annales de l'Institute Henri Poincare vol. 48, no.1, p. 151187, 2012
[ journal ] 
M. Balazs and J. Komjathy:
Order of current variance and diffusivity in the rate one totally asymmetric zero range process
Journal of Statistical Physics vol. 133, (1), pp 5978, 2008
[ journal ]
 D. Gleich, J. Komjathy, and N. Litvak:
Algorithms and Models for the Web Graph
12th International Workshop, 12th International Workshop,
WAW 2015, Eindhoven, The Netherlands, December 1011, 2015, Proceedings (Springer)
[ journal ]
Thesis
I defended my Phd in Dec 2012, under the supervision of Marton Balazs and Karoly Simon: This is my thesis (pdf).
A 24 page summary of my thesis (pdf).
CV
A short CV (updated 2023 Oct)