Related papers: A phase transition in block-weighted random maps

We show that in small and low density systems described by a lattice gas model with fixed number of particles the location of a thermodynamic phase transition can be detected by means of the distribution of the fluctuations related to an…

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which…

Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and \mu\neq 0 is triggered by the drastic change in \theta behavior. The conjecture is motivated by the…

We study the $N$-dependent behaviour of $\mathrm{2d}$ causal set quantum gravity. This theory is known to exhibit a phase transition as the analytic continuation parameter $\beta$, akin to an inverse temperature, is varied. Using a scaling…

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…

In this paper we consider coalescing random walks on a general connected graph $G=(V,E)$. We set up a unified framework to study the leading order of the decay rate of $P_t$, the expectation of the fraction of occupied sites at time $t$,…

In this conference proceeding, I discuss in detail the deconfinement to quark matter that takes place at large densities and/or temperatures. The first-order phase transition that is assumed to appear beyond a critical point gives rise to…

The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $\omega$. The law of the simple symmetric random walk up to time $n$ is modified by the exponential of the sum of…

We study the transition between phases at large $R$-charge on a conformal manifold. These phases are characterized by the behaviour of the lowest operator dimension $\Delta(Q_R)$ for fixed and large $R$-charge $Q_R$. We focus, as an…

It is natural to expect that there are only three possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of…

We analyze and simulate a two dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two dimensional box, whose boundaries…

The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories,…

We show that the Brownian continuum random tree is the Gromov-Hausdorff-Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the $d$-dimensional torus $\mathbb{Z}_n^d$ with $d>4$, the hypercube…

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature $R_w$ in a…

We study large deviations, over a long time window $T \to \infty$, of the dynamical observables $A_n = \int_{0}^{T} x^n(t) dt$, $n=3,4,\dots$, where $x(t)$ is a centered stationary Gaussian process in continuous time. We show that, for…

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…

We investigate the asymptotic behavior as $\varepsilon \to 0$ of singularly perturbed phase transition models of order $n \geq 2$, given by \begin{align} G_\varepsilon^{\lambda,n}[u] := \int_I \frac 1\varepsilon W(u)…

A linear external perturbation is introduced in the action of the partition function of the random matrix model of RNA [G. Vernizzi, H. Orland and A. Zee, Phys. Rev. Lett. 94, 168103 (2005)]. It is seen that (i). the perturbation…

Over the last half century the liquid-gas phase transition and the magnetization phase transition have come to be well understood. After an order parameter, $r$, is defined, it can be derived how $r=0$ for $T>T_c$ and how $r \propto (T_c -…