A long-standing goal of science is to accurately simulate large molecular systems using quantum mechanics. The poor scaling of current quantum chemistry algorithms on classical computers, however, imposes an effective limit of about a few dozen atoms on tr ...
We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...
Bedload transport often exhibits dual-mode behavior due to interactions of spatiotemporal controlling factors with the migrating three-dimensional bedforms (characterized by the fully developed patterns in the bed, such as alternate bars, pools, and cluste ...
Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...
In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...
Understanding looping probabilities, including the particular case of ring closure or cyclization, of fluctuating polymers (e.g., DNA) is important in many applications in molecular biology and chemistry. In a continuum limit the configuration of a polymer ...
We investigate the relationship between the N-clock model (also known as planar Potts model or DOUBLE-STRUCK CAPITAL ZN-model) and the XY model (at zero temperature) through a Gamma-convergence analysis of a suitable rescaling of the energy as both the num ...
In this thesis, we consider an anisotropic finite-range bond percolation model on Z2. On each horizontal layer {(x,i):x∈Z} for i∈Z, we have edges ⟨(x,i),(y,i)⟩ for 1≤∣x−y∣≤N with $N\in\mathbb{N ...
In this article we study imaginary Gaussian multiplicative chaos-namely a family of random generalized functions which can formally be written as e(iX(x)), where X is a log-correlated real-valued Gaussian field on R-d, that is, it has a logarithmic singula ...
In this article, we consider an anisotropic finite-range bond percolation model on Z(2). On each horizontal layer {(x, i): x is an element of Z} we have edges for 1
In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converges to nested CLE3. ...
We study the 2-dimensional Ising model at critical temperature on a simply connected subset of the square grid Z2. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to b ...
This thesis is devoted to the study of the local fields in the Ising model. The scaling limit of the critical Ising model is conjecturally described by Conformal Field Theory. The explicit predictions for the building blocks of the continuum theory (spin a ...
We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) ...
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming fro ...
Though the following topics seem unlinked, most of the tools used in this thesis are related to random walks and renewal theory. After introducing the voter model, we consider the parabolic Anderson model with the voter model as catalyst. In GÄRTNER, DEN H ...
The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The ...
We study hydrogen in the Saha regime, within the physical picture in terms of a quantum proton-electron plasma. Long ago, Saha showed that, at sufficiently low densities and low temperatures, the system behaves almost as an ideal mixture made with hydrogen ...
