Séminaire exceptionnel – 7 mars 2019 – 10h salle 250

First-passage time of non-markovian walkers and instability in the actin cortex

Nicolas Levernier – Univ. Genève, Suisse

My presentation will consist in the presentation of two independent studies. The first one deals with first-passage times (FPT) of non-markovian walkers. How long does it take for a random walker to find a target ? This question appears naturally in many context and at many scales. After a brief summary of existing results, which essentially concern Markovian (meaning memory-less) random walks, I will present the theory we have developed to deal with non-markovian random walks. I will show that, strikingly, the mean first-passage time for such a walk is fully determined by the trajectory of the walker after the FPT. Finally, I will show some application of this theory to known examples, such as the Fractional Brownian Motion. The second part will present recent works of my postdoc, and deals with a simple model of actin cortex. The actin cortex is a thin layer of actin polymers, created on the inner face of the cell membrane, and vital for the cell. I will show that describing the cortex as an extended object (that is, not using thin layer approaches), an interesting instability appear. This instability can lead directly to spatio-temporal chaos in the actin density, a feature that cannot be accounted in effective one-dimensional approaches.