Noticias en español
The Wasserstein-Martingale projection of a Brownian motion given initial and terminal marginals.
Abstract: In one of its dynamic formulations, the optimal transport problem asks to determine the stochastic process that interpolates between given initial and terminal marginals and is as close as possible to the constant-speed particle. Typically, the answer to this question is a stochastic process with constant-speed trajectories. We explore the analogue problem in the setting of martingales, and ask: what is the martingale that interpolates between given initial and terminal marginals and is as close as possible to the constant volatility particle? The answer this time is a process...
Read MoreThe contact process with fitness on Galton-Watson trees.
Abstract: The contact process is a simple model for the spread of an infection in a structured population. We consider a variant of the contact process, where vertices are equipped with a random fitness representing inhomogeneities among individuals. In this inhomogeneous contact process, the infection is passed along an edge with rate proportional to the product of the fitness values of the vertices on either end. We assume that the underlying population structure is given by a Galton-Watson tree. Recent works by Huang/Durrett and Bhamidi et al have given necessary and sufficient...
Read MoreAlmost triangular Markov chains on ℕ
Abstract: A transition matrix U on ℕ is said to be almost upper triangular if U(i,j)≥0⇒j≥i−1, so that the increments of the corresponding Markov chains are at least −1; a transition matrix L on ℕ is said to be almost lower triangular if L(i,j)≥0⇒j≤i+1, and then, the increments of the corresponding Markov chains are at most +1. In this talk I will characterise the recurrence, positive recurrence and invariant distribution for the class of almost triangular transition matrices. These results encompass the case of birth and death processes (BDP), which are famous Markov chains being...
Read MoreScaling limit of the heavy-tailed ballistic deposition model with p-sticking.
Abstract: Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. with a heavy (right) tail, and where each block sticks to the interface at the first point of contact with probability (otherwise, it falls straight down until it lands on a block belonging to the interface). We study scaling limits of the resulting interface...
Read More