Related papers: A phase transition for the heights of a fragmentat…
Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics,…
The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
We analyze the 3-parameter family of random networks which are uniform on networks with fixed number of edges, triangles, and nodes (between 33 and 66). We find precursors of phase transitions which are known to be present in the asymptotic…
We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…
We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior…
Nucleation rate computations are of broad importance in particle physics and cosmology. Perturbative calculations are often used to compute the nucleation rate $\Gamma$, but these are incomplete. We perform nonperturbative lattice…
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise the phase boundary by the existence of a metastable density,…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…
We numerically produce fully amorphous assemblies of frictionless spheres in three dimensions and study the jamming transition these packings undergo at large volume fractions. We specify four protocols yielding a critical value for the…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
The asymptotic behavior, as $n\rightarrow \infty $ of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}% (m)=(Z_{1}(m),...,Z_{N}(m)),$ with $N$ types of particles at moment…
The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase…
Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…