## National Seminar on Probability and Statistics

The next meeting of the National Seminar on Probability and Statistics will be held on April 16, 2024, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Convergence Rate for Order 1 Markov Random Walks will be delivered by Peter Gaydarov. Abstract. We examine the limiting behaviour of an order 1 Markov random walk in R2, i.e. a walk that remembers its previous step. Provided a certain symmetry of the Markovian condition, under relatively mild conditions we prove convergence to a Brownian motion and bound the rate of convergence. Therefore, an order 1 Markov condition is insufficient to alter the limiting behaviour of a random walk.