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We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromone particles and interact with them through alignment interaction. The directed pheromone particles intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail… (More)
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by nitely supported measures (the quantization problem). It is found… (More)
We consider a random walk Z (1) (K+1) n ∈ Z K+1 with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor σ 2 K = 2 K+2 with respect to the case of the classical simple random walk without constraint.
In this paper we study the Poincaré constant for the Gaussian measure restricted to D = R d − B(y, r) where B(y, r) denotes the Euclidean ball with center y and radius r, and d ≥ 2. We also study the case of the l ∞ ball (the hypercube). This is the first step in the study of the asymptotic behavior of a d-dimensional Ornstein-Uhlenbeck process in the… (More)