Related papers: Maximum and entropic repulsion for a Gaussian memb…

Ideal crystalline membranes, realized by graphene and other atomic monolayers, exhibit rich physics - a universal anomalous elasticity of the critical "flat" phase characterized by a negative Poisson ratio, universally singular elastic…

Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the…

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…

We investigate the extremal process of four-dimensional membrane models as the size of the lattice $N$ tends to infinity. We prove the cluster-like geometry of the extreme points and the existence as well as the uniqueness of the extremal…

Let $\mathcal{X}= \{X(t) : t \in \mathbb{R}^N \} $ be an isotropic Gaussian random field with real values.In a first part we study the mean number of critical points of $\mathcal{X}$ with index $k$ using random matrices tools.We obtain an…

The lecture delivered at the \emph{Current Developments in Mathematics} conference (Harvard-MIT, 2021) focused on the recent proof of the Gaussian structure of the scaling limits of the critical Ising and $\varphi^4$ fields in the marginal…

We prove that any scaling limit of a critical reflection positive Ising or $\varphi^4$ model of effective dimension $d_{\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which…

We study the extremal properties of the "integer-valued Gaussian" a.k.a.\ DG-model on the hierarchical lattice $\Lambda_n:=\{1,\dots,b\}^n$ (with $b\ge2$) of depth $n$. This is a random field $\varphi\in\mathbb Z^{\Lambda_n}$ with law…

Consider the free field on a fractal graph based on a high-dimensional Sierpinski carpet (e.g. the Menger sponge), that is, a centered Gaussian field whose covariance is the Green's function for simple random walk on the graph. Moreover…

We study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a…

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as…

Models with extra dimensions have attracted much interest recently because they may provide the solution for long standing problems in physics. One interesting and very attractive idea is that our visible universe is confined to a…

In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical…

We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length $n$ of the martingale. A consequence of the results are Gaussian couplings and a multiplier bootstrap for…

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder which has microscopic supersymmetry. It has been conjectured that in the continuum the model is described by the superconformal minimal…

We study the world-volume theory of a bosonic membrane perturbatively and discuss if one can obtain any conditions on the number of space-time dimensions from the consistency of the theory. We construct an action which is suitable for such…

In multicomponent membranes, internal scalar fields may couple to membrane curvature, thus renormalizing the membrane elastic constants and destabilizing the flat membranes. Here, a general elasticity theory of membranes is considered that…

This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…

In this thesis we provide new tools to determine and explore the Landscape of four-dimensional effective field theories originating from string and M-theory. The main aim is to introduce, within four-dimensional effective descriptions,…