The two-dimensional Yang-Mills measure is a probabilistic model describing the quantum Euclidean Yang-Mills theory in two dimensions. I will briefly describe the construction of this measure, first in lattice gauge theory, then in the continuum, revisiting a construction by Lévy (2003, 2010), then I will focus on its partition function on compact surfaces, with structure group the unitary group U(N). We will see what happens for the partition function in the large N regime, akin to random matrix theory, and in particular we will describe a so-called gauge/string duality on a torus, confirming predictions in theoretical physics by Gross and Taylor (1993). Based on a joint work with Mylène Maïda (Université de Lille).
