相关论文: A phase transition for the heights of a fragmentat…

We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…

For a critical simple exchangeable fragmentation-coagulation process in slow regime where the coagulation rate and fragmentation rate are of the same order, we show that there exist phase transitions for its boundary behavior at infinity…

We investigate the kinetics of nonlinear collision-induced fragmentation. We obtain the fragment mass distribution analytically by utilizing its travelling wave behavior. The system undergoes a shattering transition in which a finite…

We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all…

It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…

We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing…

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no…

We provide a new geometric representation of a family of fragmentation processes by nested laminations, which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation obtained by cutting a…

Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…

We consider additive functionals $X_n(\phi)$ with small toll functions on split trees and a generalization of split trees, which we call fractional split trees, where the split vector does not need to sum up to 1. These additive functionals…

We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…

Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually relies on tandem mass spectrometry to identify the thousands of…

Accurate calculations of the nucleation rate $\Gamma$ for first order phase transitions are important for determining their observable consequences in particle physics and cosmology. Perturbative calculations are often used, but they are…

We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…

The stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$ is derived by looking at the masses of the subtrees formed by discarding the parts of a $(1 + \alpha)^{-1}$--stable continuum random tree below height $t$, for $t…

We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass.…

We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…

We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…

We investigate the thermodynamical content of a cellular model which describes nuclear fragmentation as a process taking place in an excited disordered system. The model which reproduces very well the size distribution of fragments does not…

We study aggregation-fragmentation processes in which pairs of clusters can aggregate, and each cluster can break into two fragments. If the rates of aggregation and fragmentation do not depend on the masses, detailed balance does not hold,…