Jury

  • Prof. Alexandre MAUROY (UNamur), président
  • Prof. Timoteo CARLETTI (UNamur), promoteur et secrétaire
  • Prof. Malbor ASLLANI (Florida State University)
  • Prof. Renaud LAMBIOTTE (Oxford Mathematical Institute)
  • Prof. Filippo COLOMO (Università degli studi di Firenze)
  • Prof. Christian WALMSLEY HAGENDORF (UCLouvain)

Résumé

Flocks of birds, people clapping in unison or the World Wide Web are some instances of complex systems in which a large number of entities interact with each other and produce some emergent phenomena. In this thesis, we pay special attention to two such complex systems, namely crowded random walks on networks, and domino tilings and vertex models. In recent years, networks and generalizations thereof have emerged as an efficient tool to model the pattern of interactions among a set of entities. Examples include social networks, transportation networks and ecological networks. A cornerstone of network science is the interplay between network structure and dynamics on networks. Among those dynamical processes, random walks play a central role. In the first part of this thesis, we study the dynamics of multiple random walkers moving across the nodes of the network, assuming the latter to be endowed with limited available space. We characterize, both analytically and numerically, the stationary states, and we subsequently apply the latter framework to a real ecological network. In the second part of the thesis, we move on to the study of the arctic curve phenomenon arising in domino tilings of double Aztec rectangles and configurations of the six-vertex model with partial domain wall boundary conditions. The latter two models manifest in the scaling limit a spatial phase separation between ordered regions and a central disordered region. We compute the arctic curve of the aforementioned models using the tangent method.