Related papers: A recursive approach to the O(n) model on random m…

Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n -> infinity has the…

A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…

We study the asymptotic behaviour of uniform random maps with a prescribed face-degree sequence, in the bipartite case, as the number of faces tends to infinity. Under mild assumptions, we show that, properly rescaled, such maps converge in…

We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a…

We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing…

We study random bipartite planar maps defined by assigning nonnegative weights to each face of a map. We prove that for certain choices of weights a unique large face, having degree proportional to the total number of edges in the maps,…

We find that the multicritical fixed point structure of the O($N$) models is much more complicated than widely believed. In particular, we find new nonperturbative fixed points in three dimensions ($d=3$) as well as at $N=\infty$. These…

We exhibit the multicritical phase structure of the loop gas model on a random surface. The dense phase is reconsidered, with special attention paid to the topological points $g=1/p$. This phase is complementary to the dilute and higher…

We extend the peeling exploration introduced in arxiv:1506.01590 to the setting of Boltzmann planar maps coupled to a rigid $O(n)$ loop model. Its law is related to a class of discrete Markov processes obtained by confining random walks to…

In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of…

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…

We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial $Q_g^n(x)$ where $x$ is a parameter taking the number of…

Using Environmentally Friendly Renormalization, we present an analytic calculation of the series for the renormalization constants that describe the equation of state for the $O(N)$ model in the whole critical region. The solution of the…

We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…

The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…

We introduce bijections between families of rooted maps with unfixed genus and families of so-called blossoming trees endowed with an arbitrary forward matching of their leaves. We first focus on Eulerian maps with controlled vertex…

The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been conjectured that both the spin and the…

The classical spin $O(n)$ model is a model on a $d$-dimensional lattice in which a vector on the $(n-1)$-dimensional sphere is assigned to every lattice site and the vectors at adjacent sites interact ferromagnetically via their inner…

A critical dilute O($n$) model on the kagome lattice is investigated analytically and numerically. We employ a number of exact equivalences which, in a few steps, link the critical O($n$) spin model on the kagome lattice to the exactly…

We consider planar bipartite maps which are both tight, i.e. without vertices of degree $1$, and $2b$-irreducible, i.e. such that each cycle has length at least $2b$ and such that any cycle of length exactly $2b$ is the contour of a face.…