Related papers: Multiple scaling limits of $\mathrm{U}(N)^2 \times…
Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a…
We prove that uniform random quadrangulations of the sphere with $n$ faces, endowed with the usual graph distance and renormalized by $n^{-1/4}$, converge as $n\to\infty$ in distribution for the Gromov-Hausdorff topology to a limiting…
Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…
Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possess a novel large $N$ limit, where $g^2 N^3$ is held fixed. In this limit the perturbative expansion in the quartic coupling constant,…
Consider a family of random ordered graph trees $(T_n)_{n\geq 1}$, where $T_n$ has $n$ vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled…
Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the…
It is known that the classical $O(N)$ model in dimension $d > 3$ at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. For the ordinary transition the bulk and the boundary…
We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover scaling forms for the free energy and the…
We consider critical multitype Bienaym\'e trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first,…
We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…
We prove that Aldous' Brownian CRT is the scaling limit, with respect to the Gromov--Prokhorov topology, of uniform random graphs in each of the three following families of graphs: distance-hereditary graphs, $2$-connected…
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
The large-N limit of the two-dimensional U$(N)$ Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the…
We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O$(n)$ symmetric anisotropic $\phi^4$ lattice model with periodic boundary conditions in a $d$-dimensional hypercubic geometry above, at and below…
The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, called the \emph{Sinkhorn limit} of $A$. Exact formulae for the Sinkhorn…
Consider the minimum spanning tree (MST) of the complete graph with n vertices, when edges are assigned independent random weights. Endow this tree with the graph distance renormalized by n^{1/3} and with the uniform measure on its…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$, and this…
The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a…
We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for $p=p_c+\lambda\delta^{1/\nu}$, with $\nu=4/3$, as the lattice spacing $\delta \to 0$. Our proposed framework extends previous analyses for $p=p_c$, based…