Related papers: $\Gamma$-convergence and stochastic homogenisation…

Given $p\in[1,\infty)$ and a bounded open set $\Omega\subset\mathbb R^d$ with Lipschitz boundary, we study the $\Gamma$-convergence of the weighted fractional seminorm \[ [u]_{s,p,f}^p = \int_{\mathbb R^d} \int_{\mathbb R^d}…

Given a Young function $A$, $n\geq 1$ and $s\in(0,1)$ we consider the energy functional $$ \mathcal{J}_s(u)=(1-s)\iint_{\mathbb{R}^n\times \mathbb{R}^n} A\left(\frac{|u(x)-u(y)|}{|x-y|^s}\right)\frac{dxdy}{|x-y|^n}. $$ Without assuming the…

A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…

We study periodic homogenization by Gamma-convergence of some singular integral functionals related to nonlinear elasticity.

In this note, by using the result in one variable, we obtain asymptotic expansions of oscillatory integrals for certain multivariable phase functions with {\bf degenerate} singular points. Moreover by using this result, we have asymptotic…

We study the large scale equilibrium behavior of Van der Waals-Cahn-Hilliard phase transitions in stationary ergodic media. Specifically, we are interested in free energy functionals of the following form \begin{equation*}…

We investigate equilibrium and steady-state non-equilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width ~\Gamma via a Coulomb interaction U and a hybridization t'. In order to study the…

We investigate the superfluid-to-normal zero temperature quantum phase transitions of asymmetric two-component Fermi gases as a function of the chemical potential imbalance $h$. The calculations are performed for homogeneous and trapped…

In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under \emph{linear} growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general…

We study the problem of recovering a function of the form $f(x) = \sum _{k\in \mathbb{Z} } c_k e^{-(x-k)^2}$ from its phaseless samples $|f(\lambda )|$ on some arbitrary countable set $\Lambda \subseteq \mathbb{R} $. For real-valued…

In this paper we propose a method to study the Functional Renormalization Group at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with…

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

We are concerned in this paper with the functional asymptotic behaviour of the sequence of stochastic processes T_{n}(f)=\sum_{j=1}^{j=k}f(j)(\log X_{n-j+1,n}-\log X_{n-j,n}), indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}…

We study the resurgence properties of the coefficients $C_n(\tau)$ appearing in the asymptotic expansion of the incomplete gamma function within the transition region. Our findings reveal that the asymptotic behaviour of $C_n(\tau)$ as…

Variational models of phase transitions take into account double-well energies singularly perturbed by gradient terms, such as the Cahn-Hilliard free energy. The derivation by $\Gamma$-convergence of a sharp-interface limit for such energy…

Consider a sequence X_k=\sum_{j=0}^{\infty}c_j\xi_{k-j}, k\geq 1, where c_j, j\geq 0, is a sequence of constants and \xi_j, -\infty <j<\infty, is a sequence of independent identically distributed (i.i.d.) random variables (r.v.s) belonging…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

Inspired by Lin-Pan-Wang (Comm. Pure Appl. Math., 65(6): 833-888, 2012), we continue to study the corresponding time-independent case of the Keller-Rubinstein-Sternberg problem. To be precise, we explore the asymptotic behavior of…

Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional,…

We investigate the asymptotic behavior in the sense of $\Gamma(L^1_{loc})$-convergence as $s\to1^-$ of anisotropic non local $s$-fractional perimeters defined with respect to general anisotropic integration kernels $k_s(\cdot)$, under the…