Lukas Lüchtrath

Introduction

I am currently a post-doc in Benedikt Jahnel's group Probabilistic Methods for Dynamic Communication Networks at Wias Berlin. My main area of interest is probability theory; especially spatial stochastics, complex networks and percolation. I did my PhD under the supervision of Peter Mörters at the University of Cologne.
I did my Master's in mathematics in 2018 and my Bachelor's in business mathematics in 2014 at University of Cologne.

Preprints

• Maximising homomorphism counts between digraphs
  with Christian Mönch
  arXiv preprint: 2603.18847,
• Age-dependent random connection models with arc reciprocity: clustering and connectivity
  with Christian Mönch
  arXiv preprint: 2603.16824,
• Detection, coverage and percolation in dynamic Boolean models with random radii based on α-stable processes
  with Peter Gracar, Benedikt Jahnel and Anh Duc Vu
  arXiv preprint: 2602.22109,
• Oriented bond-site percolation in random environment and contact processes with periodic recovery
  with Benedikt Jahnel and Anh Duc Vu
  arXiv preprint: 2507.00329,
• Phase transitions for contact processes on sparse random graphs via metastability and local limits
  with Benedikt Jahnel and Christian Mönch
  arXiv preprint: 2505.22471,
• Phase transitions for contact processes on one-dimensional networks
  with Benedikt Jahnel and Christian Mönch
  arXiv preprint: 2501.16858,
• The Erdős-Rényi random graph conditioned on every component being a clique
  with Martijn Gösgens, Elena Magnanini, Marc Noy, and Élie de Panafieu
  arXiv preprint: 2405.13454,
• Cluster sizes in subcritical soft Boolean models
  with Benedikt Jahnel and Marcel Ortgiese
  arXiv preprint: 2404.13730, short video summary

Published and accepted Papers

• Subcritical annulus crossing in spatial random graphs
  with Emmanuel Jacob and Benedikt Jahnel,
  arXiv preprint: 2411.10333, to appear in Advances in Applied Probability 58.4 (December, 2026), short video summary
• First contact percolation
  with Benedikt Jahnel and Anh Duc Vu
  Bernoulli 32(2) (2026). doi: 10.3150/25-BEJ1922, available on arXiv:2412.14987,
• All spatial random graphs with weak long-range effects have chemical distance comparable to Euclidean distance
  J. Theor. Probab. 39:12 (2026). doi: 10.1007/s10959-025-01467-0
• Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension
  with Peter Gracar and Christian Mönch
  Electron. J. Probab. 30: 1-29 (2025). doi: 10.1214/25-EJP1399
• A very short proof of Sidorenko's inequality for counts of homomorphism between graphs
  with Christian Mönch
  B. Aust. Math. Soc. (2025):1-5. doi:10.1017/S000497272500019X
• Percolation phase transition in weight-dependent random connection models
  with Peter Gracar and Peter Mörters
  Adv. Appl. Probab. (2021), 53(4), 1090-1114. doi:10.1017/apr.2021.13
• Preferential attachment with location-based choice: Degree distribution in the noncondensation phase
  with Arne Grauer and Mark Yarrow
  J. Stat. Phys. (2021), 184, Doi: 10.1007/s10955-021-02782-6
• The age-dependent random connection model
  with Peter Gracar, Arne Grauer, and Peter Mörters
  Queueing Syst. (2019), 93(3), 309-331, DOI: 10.1007/s11134-019-09625-y

Conference Proceedings

• The Directed Age-Dependent Random Connection Model with Arc Reciprocity,
  with Christian Mönch
  in Dewar, M., et al. Modelling and Mining Networks. WAW 2024. Lecture Notes in Computer Science, vol 14671. Springer, Cham.
• The emergence of a giant component in one-dimensional inhomogeneous networks with long-range effects,
  with Peter Gracar and Christian Mönch
  in Algorithms and Models for the Web Graph, M. Dewar, P. Prałat, P. Szufel, F. Théberge, and M. Wrzosek, Eds., Cham: Springer Nature Switzerland, 2023, pp. 19–35.

Past talks

• The contact process on one-dimensional scale-free networks
  Seminar Stochastic geometry, KIT, February 2026.
• The contact process on one-dimensional scale-free networks
  at Probability Seminar, University of Leeds, September 2025.
• The contact process on one-dimensional scale-free networks
  Bath Probability Lectures 2025 , Bath, September 2025
• What is...? Geometric inhomogeneous random graphs
  at DFG-SPP2265 Random geometric systems Fourth annual conference, Berlin, June 2025.
• The contact process on one-dimensional scale-free networks
  at Workshop Recent Advances in Evolving and Spatial Random Graphs, Bayrischzell, June 2025.
• Cluster sizes in subcritical soft Boolean models
  at German probability and statistic days 2025, Session: S 2 (2): Spatial stochastics, disordered media, and complex networks, Dresden, March 2025.
• Existence of an extinction phase for the contact process on one-dimensional networks with heavy-tailed degree distribution
  at Workshop Stochastic Processes on Random Geometries, February 2025.
• Cluster sizes in subcritical soft Boolean models
  at Geneva Mathematical Physics Seminar, December, 2024.
• A random cluster graph
  at Oberseminar Stochastik of the University of Cologne, October 2024.
• The Directed Age-Dependent Random Connection Model with Arc Reciprocity
  at WAW 2024 in Warsaw, June 2024.
• Cluster sizes in soft Boolean models
  at Probability and Analysis 2024 in Bedlewo, May 2024.
• The random cluster graph
  at Workshop Frauenchiemsee 2024 of the DFG-funded Scientific Network Stochastic Processes on Evolving Networks, January 2024.
• The random cluster graph
  at Probability Seminar, University of Leeds, November 2023.
• The random cluster graph
  at Probability and Statistics Seminar Series of University of Sheffield, November 2023.
• Euclidean Diameter of the soft Boolean model
  at 29th Nordic Congress of Mathematics, Aalborg University, July 2023
• The emergence of a giant component in one-dimensional inhomogeneous networks with long-range effects
  at 18th Workshop on Algorithms and Models for Web Graphs, Fields Institute Toronto, May 2023
• Finite percolation thresholds in one dimensional inhomogeneous random graphs
  at German probability and statistic days 2023, University of Essen, March 2023
• Evolving networks, their limits and global properties
  at Oberseminar Stochastik of the University Augsburg, January 2023
• Percolation in weight-dependent random connection models
  at RandNET Summer School and Workshop on Random Graphs at Eindhoven, August 2022
• The various phases of long-range inhomogeneous percolation
  at Seminar Interacting Random Systems of WIAS Berlin, June 2022
• The various phases of long-range inhomogeneous percolation
  at Workshop: Mathematics of large networks (Erdös Center, Budapest), May 2022
• Non-triviality of the phase transition in inhomogeneous long-range percolation in dimension one
  at SPP2265 Workshop Random spatial networks, March 2022
  
• Percolation phase transition in weight-dependent random connection models
  at Projet ANR GrHyDy: Workshop on geometric random graph models and percolation, Oktober 2021.
  
• Percolation phase transition in weight-dependent random connection models
  Video talk for the Stochastik-Tage Mannheim, October 2021.
  
• Percolation phase transition in weight-dependent random connection models
  at Prob-Lab Seminar of the University of Bath, September 2021.
  
• The age-dependent random connection model
  at Probability and Statistics Seminar Series of University of Sheffield, April 2019.
  With Arne Grauer

Co-organised events

• Workshop: Dynamic spatial random systems, 29 - 31 January 2024, Berlin
• SPP2265 Summer School: Processes on Random Geometric Graphs, 12 - 16 September 2022, Cologne
• SPP2265 Workshop Random spatial networks, 14 - 17 March 2022, Bonn

Teaching

Current semester (Sommersemester 26):

Particle systems with contact interaction, TU Berlin

Former semesters:

• Random graphs (lecture + seminar)
• Versicherungsmathematik

Assisted lectures:

• Statistische Mechanik
• Seminar "Punktprozesse"
• Mathematik für Lehramtsstudierende I & II
• Stochastische Finanzmathematik
• Wahrscheinlichkeitstheorie I & II
• Einführung in die Stochastik
• Markovprozesse
• Lineare Algebra I & II