Related papers: Subsequential tightness of the maximum of two dime…
We consider the discrete Ginzburg-Landau field with potential satisfying a uniform convexity condition, in the critical dimension $d=2$, and prove that its maximum over boxes of sidelength $N$, centered by an explicit $N$-dependent…
We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long-standing conjecture. The proof combines a recent observation of…
We consider a family of centered Gaussian fields on the d-dimensional unit box, whose covariance decreases logarithmically in the distance between points. We prove tightness of the recentered maximum of the Gaussian fields and provide…
The $\mathcal{N}=2$ Landau--Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional…
In this paper we prove the convergence for all time for a Ginzburg- Landau type approximation of a simplified Ericksen-Leslie model in two dimension. Moreover, we are able to show that the singular set consists in at most finitely many…
We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, is tight; this still leaves open the…
We consider the two-dimensional Gaussian Free Field on a box of side length $N$, with Dirichlet boundary data, and prove the convergence of the law of the recentered maximum of the field.
We analyze Ginzburg--Landau minimization problems in two dimensions with either a strong or weak" tangential boundary condition. These problems are motivated by experiments in liquid crystal with boundary defects. In the singular limit when…
We survey on the recent progress toward mirror symmetry between Landau-Ginzburg models.
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on…
For $0<\beta<6\pi$, we prove that the distribution of the centred maximum of the $\epsilon$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as $\epsilon \to 0$. Our…
We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a…
We study two dimensional massless field in a box with potential $V\left( \nabla \phi \left( \cdot \right) \right) $ and zero boundary condition, where $V$ is any symmetric and uniformly convex function. Naddaf-Spencer and Miller proved the…
We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double…
We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that…
A convergent approximation is proposed for a mean field density-density correlation function in a system with a two-phase interface. It is based on a fourth-order expansion of the Hamiltonian in terms of fluctuations around the equilibrium…
We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_N\subset Z^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that…
We continue the study of the maximum of the scale-inhomogeneous discrete Gaussian free field in dimension two. In this paper, we consider the regime of weak correlations and prove the convergence in law of the centred maximum to a randomly…
We show that Blokhuis' quadratic upper bound for two-distance sets is sharp over finite fields in almost all dimensions. Our construction complements Lison\v{e}k's higher-dimensional maximal constructions that were carried out in Lorentz…
Using the nonlinear Ginzburg-Landau theory we investigated the dependence of the magnetic coupling between two concentric mesoscopic superconducting rings on their thickness. The size of this magnetic coupling increases with the thickness…