Julia Komjathy


     Hello visitor!
     This is my fairly minimalistic website, up-to-date on 14 April 2022.
     I am an associate professor at the TU Delft in the Applied Probability group.




     My address:                

     Delft University of Technology
     Department Elektrotechniek, Wiskunde en Informatica (EWI)
     Delft Institute of Applied Mathematics (DIAM)
     Applied Probability Group
     Mekelweg
     2628CD Delft
     The Netherlands

      email: j.[last name] at tudelft dot nl,
      office phone: not really known to me...
     EWI building, room 7.050

This picture is about 10 years old now..., about to be replaced.

Research interests
     
  • random graph models of complex networks
         
  • spatial random graphs, hyperbolic random graphs
         
  • topology and structure of weighted random graphs
         
  • `explosion' in weighted random graphs
         
  • epidemic spread on networks
         
  • branching processes


    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, 3-7 June in Warsaw
    ``WAW 2024: 19th Workshop on Modelling and Mining Networks''
    I will speak at the Discrete Probability Days, Barcelona 16-20 Oct 2023
    Discrete Probability Days at CRM


    Phd students, postdocs
         
  • Enrico Baroni.
          Thesis: Universality of weighted scale-free configuration model
          jointly with Remco van der Hofstad, award date: 6 Feb 2017
          [ link to Enrico's thesis at Tue library ]
         
  • Viktoria Vadon.
          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 ]
         
  • Daniel Olah.
          Thesis: Reliable geometric spanners
          jointly with Kevin Buchin, award date: 10 July 2021
          [ link to Daniel's thesis at Tue library ]
         
  • Joost Jorritsma.
          Thesis: Distances and components in scale-free random graph models
          graduated on 18 April 2023
          [ link to Joost's website ]
          [ link to Joost's thesis at Tue library ]
         
  • Zsolt Bartha.
          postdoc. Topic: Contact processes and k-cores.
          Zsolt is currently at the Renyi institute in Budapest.


    My latest preprints and papers

    1.       Z. Bartha, J. Komjathy, D.Valesin
            Degree-dependent contact processes
            [ arXiv ]

            Short description: The degree-dependent 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 Galton-Watson 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 power-law 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: k-cores.

    2.       J. Komjathy, J. Lapinskas, J.Lengler, U. Schaller
            Four universal growth regimes in degree-dependent first passage percolation on spatial random graphs I
            [ arXiv ]

            Short description: One-dependent 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 scale-free 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 sub-explosive phases.

    3.       J. Komjathy, J. Lapinskas, J.Lengler, U. Schaller
            Four universal growth regimes in degree-dependent 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.

    4.       J. Jorritsma, J. Komjathy, D. Mitsche
            Cluster-size decay in supercritical kernel-based 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 (d-1)/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 long-range edges and `superspreaders' (hubs). We identify when and how this structural inhomogeneity deforms the surface-tension driven clusters: they are spread-out in space, governed either by long-range edges or by superpreaders, or both, which implies that the stretch-exponent changes to four possible values, which constitutes a phase diagram for cluster size-decay. The stretch-exponents also give information on the topology inside the giant component, and govern the speed of lower-large deviations for the size of the giant.

    5.       J. Jorritsma, J. Komjathy, D. Mitsche
            Cluster-size decay in supercritical long-range percolation
            [ arXiv ]

            Short description:In this paper we study cluster sizes in long-range 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 (d-1)/d, and 2-alpha, where alpha governs the long-range connection probability. In this paper we prove this result when the minimum is (d-1)/d, which gives the part of the phase diagram that was left open in the paper "Cluster-size decay in supercritical kernel-based spatial random graphs" above.

    6.       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 Covid-inspired paper investigates the effect of the initial seeding of an epidemic on the final outbreak size. Starting an epidemic from the best-connected 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 data-driven 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.

    7.       J. Jorritsma, and J. Komjathy
            Distance evolutions in growing preferential attachment graphs (2022)
            Annals of Applied Probability, 32(6): 4356-4397 (Dec 2022).
            [ journal ] [ arXiv ]
            Short description: This paper is the first to study how graph (and weighted) distances in preferential attachment-type models shrink as the graph grows around two vertices chosen uniformly at random at some time t. It shows that the graph-distance stays in a tight strip around the main order term for all later times, and eventually settles on 2.

    Full list of publications and preprints

          up to date on 14 April 2022
    1.       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 ]

    2.       J. Jorritsma, and J. Komjathy
            Distance evolutions in growing preferential attachment graphs (2022)
            Annals of Applied Probability, 32(6): 4356-4397 (Dec 2022)
            [ journal ]       [ arXiv ]

    3.       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, 406-461 (2022)
            [ journal ] [ arXiv ]

    4.       G. Odor, D. Czifra, J. Komjathy, L. Lovasz, and M. Karsai
            Longer-term seeding effects on epidemic processes: a network approach
            Scientia et Securitas Vol 2, Issue 4, p 409-417 (2022)
            [ journal, open access ]

    5.       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 ]

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

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

    8.       J. Komjathy, J. Lapinskas and J. Lengler
            Stopping explosion by penalising transmission to hubs in scale-free spatial random graphs (2021)
            Annales de l'Institute Henri Poincare, Vol. 57 (4) p:1968-2016, (Nov 2021)
           [ journal ] [ arXiv ]

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

    10.       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 ]

    11.       J. Jorritsma, and J. Komjathy
            Weighted distances in scale-free preferential attachment models (2020)
            Random Structures and Algorithms, Vol 57 (3): 823-859 (2020)
            [ journal ] [ arXiv ]

    12.       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 1309-1367 (2020)
            [ journal ] [ arXiv ]

    13.       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 ]

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

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

    16.       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 ]

    17.       R. van der Hofstad and J. Komjathy
            Explosion and distances in scale-free percolation (2017 June)
            [ arXiv ]

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

    19.       R. van der Hofstad and J. Komjathy
            When is a scale-free graph ultra-small?
            Journal of Statistical Physics Vol. 169 (2), pp 223 - 264, (2017).
            [ journal ] [ arxiv ]

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

    21.       J. Komjathy
            Explosion of Crump-Mode-Jagers branching processes (2016 Feb)
            [ arXiv ]

    22.       J. Komjathy and V. Vadon
            First passage percolation on the Newman-Watts small world model
            Journal of Statistical Physics, vol. 162, Issue 4, p. 959-993 (2016)
            [ arXiv ] [ journal ]

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

    24.       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. 1-48 (2015)
            [ arXiv] [ journal ]

    25.       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. 101-121 2014.
            [ arXiv ] [ journal ]

    26.       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. 865-902. 2016.
            [ arXiv ] [ journal ]

    27.       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. 1780-1826. (2015)
            [ arXiv ] [ journal ]

    28.       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 ]

    29.       I. Kolossvary and J. Komjathy:
           First passage percolation on inhomogeneous random graphs,
           Advances of Applied Probability vol 47 No. 2 p. 589-610. (2015)
            [ arXiv ] [ journal ]

    30.       J. Komjathy and Y. Peres:
            Mixing and relaxation time for random walk on wreath product graphs,
            Electronic Journal of Probability, vol. 18, 71, p. 1-23, (2013)
            [ arXiv ] [ journal ]

    31.       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. 1140-1160 (2014)
            [ arXiv ] [ journal ]

    32.       J. Komjathy and K. Simon:
            Generating hierarchical scale free graphs from fractals,
            Chaos, Solitons and Fractals, vol. 44, p. 651-666, (2011)
            [ arXiv ] [ journal ]

    33.       M. Balazs and J. Komjathy and T. Seppalainen:
            Fluctuation bounds in the exponential bricklayers process,
            Journal of Statistical Physics, vol. 147, no. 1, p. 35-62, 2012
            [ journal ]

    34.       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. 151-187, 2012
            [ journal ]

    35.       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 59-78, 2008
            [ journal ]
    Edited Proceedings
           
    1. 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 10-11, 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)