Related papers: Coalescence on the real line
We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range…
A colouring of the edges of an $n \times n$ grid is said to be \emph{reconstructible} if the colouring is uniquely determined by the multiset of its $n^2$ \emph{tiles}, where the tile corresponding to a vertex of the grid specifies the…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
A rainbow subgraph of an edge-coloured graph has all edges of distinct colours. A random d-regular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
Let $R(C_n)$ be the Ramsey number of the cycle on $n$ vertices. We prove that, for some $C > 0$, with high probability every $2$-colouring of the edges of $G(N,p)$ has a monochromatic copy of $C_n$, as long as $N\geq R(C_n) + C/p$ and $p…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find…
We study a restricted form of list colouring, for which every pair of lists that correspond to adjacent vertices may not share more than one colour. The optimal list size such that a proper list colouring is always possible given this…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
In the classical two-sample problem, the conventional approach for testing distributions equality is based on the difference between the two marginal empirical distribution functions, whereas a test for independence is based on the contrast…
The microscopic dependence of glassy equilibration on sample history, both the initial configuration and the specific sequence of random noise, is examined. The temporal evolution of spin configurations in a two-dimensional Ising spin glass…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
We use direct numerical simulations and scaling arguments to study coarsening in binary fluid mixtures with a conserved order parameter in the droplet-spinodal regime -- the volume fraction of the droplets is neither too small nor symmetric…
This paper describes a mathematical model for the spread of a virus through an isolated population of a given size. The model uses three, color-coded components, called molecules (red for infected and still contagious; green for infected,…
A graph is said to be interval colourable if it admits a proper edge-colouring using palette $\mathbb{N}$ in which the set of colours incident to each vertex is an interval. The interval colouring thickness of a graph $G$ is the minimum $k$…