Lukas Lüchtrath

Events

SPP2265 Summer School: Processes on Random Geometric Graphs, 12 - 16 September 2022, Cologne

SPP2265 Workshop Random spatial networks, 14 - 17 March 2022, Bonn

Introduction

I am a PhD student and research assistant in the research group of Prof. Peter Mörters at the University of Cologne. My main area of interest is probability theory. I am currently working on random networks and their geometry.
I did my Master's in mathematics in 2018 and my Bachelor's in business mathematics in 2014 at University of Cologne.

A cv can be found here.

Published Papers and Preprints

• Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension
  with Peter Gracar and Christian Mönch
  arXiv preprint: 2203.11966
• Percolation phase transition in weight-dependent random connection models
  with Peter Gracar and Peter Mörters
  Advances in Applied Probability (2021), 53(4), 1090-1114. doi:10.1017/apr.2021.13
  Access to ArXiv preprint
• Preferential attachment with location-based choice: Degree distribution in the noncondensation phase
  with Arne Grauer and Mark Yarrow
  Journal of Statistical Physics (2021), 184, Doi: 10.1007/s10955-021-02782-6
• The age-dependent random connection model
  with Peter Gracar, Arne Grauer and Peter Mörters
  Queueing Systems (2019), 93(3), 309-331, DOI: 10.1007/s11134-019-09625-y

Talks

• Non-triviality of the phase transition in inhomogeneous long-range percolation in dimension one
  SPP2265 Workshop Random spatial networks, March 2022
  
• Percolation phase transition in weight-dependent random connection models
  Projet ANR GrHyDy: Workshop on geometric random graph models and percolation, Oktober 2021.
  
• Percolation phase transition in weight-dependent random connection models
  Contributed video talk for the Stochastik-Tage Mannheim, Oktober 2021.
  
• Percolation phase transition in weight-dependent random connection models
  Invited Speaker in the Prob-Lab Seminar of the University of Bath, September 2021.
  
• The age-dependent random connection model
  Invited speaker in the Probability and Statistics Seminar Series of University of Sheffield, April 2019.
  With Arne Grauer

Teaching

Current semester:

• Running the excercises for the lecture Statistische Mechanik



Former semesters:

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