Interests

Random graphs and hypergraphs, random trees, concentration inequalities

PhD thesis

Inequalities for sums of random variables: a combinatorial perspective, Adam Mickiewicz University (2012). PDF file (corrected version from 12.07.2012).

Publications

Journal papers

1. D. Dzindzalieta, T. Juškevičius, M. Šileikis. Optimal Probability Inequalities for Random Walks Related to Problems in Extremal Combinatorics, SIAM J. Discrete Math. 26-2 (2012), pp. 828–837. preprint, paper

2. M. Šileikis. On the Upper Tail of Counts of Strictly Balanced Subgraphs, Electron. J. Combin. 19-1 (2012), P4. paper

3. A. Dudek, A. Frieze, A. Ruciński, M. Šileikis. Approximate counting of regular hypergraphs via switchings, Inform. process. lett. 113 (2013), pp. 785–788. preprint, paper

4. A. Dudek, A. Frieze, A. Ruciński, M Šileikis. Loose Hamilton Cycles in Regular Hypergraphs, Combin. Probab. Comput. 24 (2015) Special Issue 01, pp. 179–194. preprint, paper

5. A. Dudek, A. Frieze, A. Ruciński, M Šileikis. Embedding the Erdős-Rényi Hypergraph into the Random Regular Hypergraph and Hamiltonicity, J. Comb. Theory B 122 (2017), pp. 719–740. preprint, paper

6. T. Łuczak, K. Mieczkowska. M. Šileikis. On maximal tail probability of sums of nonnegative, independent and identically distributed random variables, Statistics & Probability Letters 129 (2017), pp. 12–16. preprint, paper.

7. C. Holmgren, S. Janson, M. Šileikis. Multivariate normal limit laws for the numbers of fringe subtrees in m-ary search trees and preferential attachment trees, Electron. J. Combin. 24-2 (2017), P2.51. paper, extended abstract from AofA 2016 conference

8. M. Šileikis, L. Warnke. A counterexample to the DeMarco-Kahn Upper Tail Conjecture, Random Structures & Algorithms 55-4 (2019), pp. 775–794. preprint, paper

9. D. Ralaivaosaona, M. Šileikis, S. Wagner. A central limit theorem for almost local additive tree functionals, Algorithmica 82 (2020), pp. 642–679, DOI:10.1007/s00453-019-00622-4. preprint, paper

10. M. Šileikis, L. Warnke. Upper tail bounds for Stars, Electron. J. Combin. 27-1 (2020), P1.67. preprint, paper

11. J. Hladký, C. Pelekis, M. Šileikis. A limit theorem for small cliques in inhomogeneous random graphs. Journal of Graph Theory,  97-4 (2021), pp. 578-599. DOI:10.1002/jgt.22673 . preprint, paper

12. M. Šileikis, L. Warnke. Counting extensions revisited, Random Structures & Algorithms, 61-1 (2022), pp. 3-30. DOI:10.1002/rsa.21050 preprint, paper

13.  T. Klimošová, Chr. Reiher, A. Ruciński, M. Šileikis. Sandwiching biregular random graphs, Combin. Probab. Comput., 32-1 (2023) pp. 1-44. DOI:10.1017/S0963548322000049 preprint, paper

14. F. Garbe, J. Hladký, M. Šileikis, F. Skerman. From flip processes to dynamical systems on graphons, accepted to Annales de l’Institut Henri Poincaré (B) Probability and Statistics. preprint, list of accepted papers

15. P. Araújo, J. Hladký, E. K. Hng, M. Šileikis, Prominent examples of flip processes, Random Structures & Algorithms,64-3 (2024) pp. 692-740.  DOI:10.1002/rsa.21192 preprint, paper

Preprints

16. P. Araújo, S. Griffiths, M. Šileikis, L. Warnke. Extreme local statistics in random graphs: maximum tree extension counts, submitted. preprint

Conference proceedings

1. D. Ralaivaosaona, M. Šileikis, S. Wagner. Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees. In: Ward, M.; Fill, J. (eds) 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics, vol 110 (2018), paper 33. Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Schloss Dagstuhl. paper

2. V. Blažej, M. Opler, M. Šileikis, P. Valtr. On the Intersections of Non-homotopic Loops. In: Mudgal A., Subramanian C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science, vol 12601  (2021). Springer, Cham. paper

3. V. Blažej, M. Opler, M. Šileikis, P. Valtr. Non-homotopic Loops with a Bounded Number of Pairwise Intersections. In: Purchase H.C., Rutter I. (eds) Graph Drawing and Network Visualization. GD 2021. Lecture Notes in Computer Science, vol 12868 (2021). Springer, Cham. preprint with appendix, paper

Talks

Invited

• Graph flip processes related to dynamical systems, NORDSTAT 2023, Gothenburg 

• Small clique counts in dense inhomogeneous random graphs, Prague Stochastics 2019, Prague, August 2019, slides

• Embedding G(n,p) into the random regular graph, Atlanta Lecture Series, Georgia Tech, Atlanta, USA, 2017, slides

• Embedding the Uniform Random Graph into the Bipartite Regular Random Graph, minisymposium Discrete Random Processes at 2018 SIAM Conference on Discrete Mathematics, University of Colorado, Denver, 4-8 June 2018, slides

• Embedding G(n,p) into the random regular graph, special session Graphs, Hypergraphs and Set Systems of the Meeting of the Catalan, Spanish, Swedish Math Societies, Umea university, Sweden, 2017

Other

• Ekstremalios lokalios statistikos atsitiktiniuose grafuose, Institute of Computer Science seminar, Vilnius University, 2023

• Maximum local tree counts in G(n,p), Seminar of the combinatorial group, ICS of Czech Academy of Sciences, Prague, 2023, notes

• Flip processes on dense graphs and dynamical systems, Noon lectures, Charles University, Prague, April 2022

• Graph flip processes, Random Structures and Algorithms, Gniezno, Poland, August 2022

• Limit distribution of subgraph counts in dense inhomogeneous random graphs, seminar of AMU Poznań, Poland (online), notes

• On the upper tail of subgraph counts in sparse G(n, p), Random Structures and Algorithms, Zurich, Switzerland, 2019, abstract, slides

• Small subgraph counts in the binomial random graph: a survey. Extremal graph theory group seminar, CSI CAS, Prague, 26 October 2018

• Subgraph counts in random graphs, Combinatorical and Algebraic Structures Seminar, FJFI, Czech Technical University, Prague, 2 October 2018 slides

• Limit Distribution of Clique Counts in Dense Inhomogeneous Graphs, 12th International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius, Lithuania, 2-6 July 2018, slides

• Counterexamples to the Demarco-Kahn conjecture on the upper tail of subgraph counts, STAR Workshop in Random Graphs, Radboud University Nijmegen, The Netherlands, 12-13 April 2018, slides

• Limit distribution of clique counts in dense inhomogeneous graphs, Workshop Graph limits in Bohemian Switzerland, Czech Republic, 26-30 March 2018, slides

• Small subgraph counts in random graphs: a survey, Georgia Tech Combinatorics Seminar, Atlanta, USA, 2017

• Embedding the Erdős–Rényi graph into the random regular graph, Random Structures & Algorithms, Gniezno, Poland, 2017

• Using Pólya Urns to Show Normal Limit Laws for Fringe Subtrees in m-ary Search Trees and Preferential Attachment Trees, SIAM Conference on Discrete Mathematics, Atlanta 2016, slides

• Concentration of Extension Counts in G(n,p), SIAM Conference on Discrete Mathematics, Atlanta 2016, slides

• Random graphs: sandwiching, subgraph counts, extension statements, Seminar of Discrete Mathematics and Optimization, Graz University of Technology, 2015

• Embedding the binomial random graph in the regular random graph, Random Structures & Algorithms, Pittsburgh, USA, 2015. Abstract

• Embedding the Binomial Hypergraph into the Random Regular Hypergraph, Combinatorial Theory seminar, University of Oxford, June 2015.

• Embedding the Erdos-Renyi random graph in the d-regular random graph, 11th International Vilnius Conference on Probability Theory and Mathematical Statistics, July 2014.

• Half-sandwich of random graphs, Scientific program Graphs, Hypergraphs and Computing, Institut Mittag-Leffler, Djursholm, May 2014.

• Regular Hypergraphs: Asymptotic Counting and Loose Hamilton Cycles, Eurocomb, Pisa, September 2013. slides, Extended Abstract

• On the upper tail of strictly balanced subgraph counts, Poznań-Berlin Seminar, Będlewo, June 2011. slides