We consider inhomogeneous Erd\H{o}s-R\'enyi graphs. We suppose that the maximal mean degree d satisfies d \ll \log n. We characterize the asymptotic behavior of the n^{1−o(1)} largest...

# Publications

## Pages

We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We...

We consider systems of N bosons in a box with volume one, interacting through a repulsive two-body potential of the form \kappa N^{3\beta-1} V(N^\beta x). For all 0 < \beta < 1, and for...

We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. For the Erd\H{o}s-R\'enyi...

In this paper, we show that the interfaces in FK Ising model in any domain with 4 marked boundary points and wired--free--wired--free boundary conditions conditioned on a specific internal arc...

The Fermi edge singularity (FES) is a prominent manifestation of the Coulomb interaction. It can be observed in a controllable way by studying the transport through a quantum dot (QD), which is...

We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form H = H_V - i C^* C, where H_V = H_0 + V is self-adjoint and C is a bounded...

The existence of weak solutions to the stationary Navier-Stokes equations in the whole plane \mathbb{R}^2 is proven. This particular geometry was the only case left open since the work of Leray...

Motivated by applications for non-perturbative topological strings in toric Calabi--Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of...

We prove that the homotopy category of topological operads P satisfying P(0)=∗ forms a full subcategory of the homotopy category of all topological operads. We more precisely establish that we...

We express the rational homotopy type of the mapping spaces *\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q}) *of the little discs operads in terms of graph complexes. Using known...

In this paper, we describe a surprising link between the theory of the Goldman-Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara-Vergne (KV) problem in Lie theory. Let Σ be an...