4 papers
Once-Reinforced and Self-Interacting Random Walks beyond exchangeability
Andrea Collevecchio, Pierre Tarrès
We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove l…
Continuous-time vertex-reinforced random walks on complete-like graphs
Shuo Qin, Pierre Tarres
We introduce the continuous-time vertex-reinforced random walk (cVRRW) as a continuous-time version of the vertex-reinforced random walk (VRRW), which might open a new perspective…
Non-convergence to unstable equilibriums for continuous-time and discrete-time stochastic processes
Olivier Raimond, Pierre Tarres
We prove non-convergence theorems towards an unstable equilibrium (or a trap) for stochastic processes. The processes we consider are continuous-time or discrete-time processes and…
What is the difference between a square and a triangle?
V. Limic, P. Tarres
We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarrès (2007). L…