Related papers: Random polymers on the complete graph
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched…
This paper describes directed polymer on general time-correlated random field. Law of large numbers, existence and smoothness of limiting free energies are proved at all temperature. We also display the delocalized-localized transition, via…
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the…
We study a model of directed polymers with an exponentially recurrent Markov chain and an indefinitely divisible random environment. We prove that the normalized partition function converges exponentially fast towards zero at all…
We consider directed polymer models involving multiple non-intersecting random walks moving through a space-time disordered environment in one spatial dimension. For a single random walk, Alberts, Khanin and Quastel proved that under…
A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by…
We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
We study cumulants of numbers of $q$-step walks on Erd\"os-R\'enyi-type random graphs of long-range percolation radius model in the limit when the number of vertices $N$, concentration $c$, and the interaction radius $R$ tend to infinity.…
Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaos Solitons & Fractals, 139,110003 (2020)]. We determine the conditions for having fat-tailed…
We prove a non-stationary analog of the Furstenberg Theorem on random matrix products (that can be considered as a matrix version of the law of large numbers). Namely, under a suitable genericity conditions the sequence of norms of random…
Consider a family of random walks $S_n^{(a)}=X_1^{(a)}+\cdots+X_n^{(a)}$ with negative drift $\mathbf E X_1^{(a)}=-a<0$ and finite variance $\mbox{var}(X_1^{(a)})=\sigma^2<\infty$.Let $M^{(a)}=\max_{n\ge 0} S_n^{(a)}$ be the maximums of the…
We consider the complex polymer system, consisting of ring polymer connected to the $f_1$-branched star-like structure, in good solvent in presence of structural inhomogeneities. We assume, that structural defects are correlated at large…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…
We analyse bead--spring polymers coupled to Navier--Stokes turbulence in ultra--dilute solutions at Weissenberg number \(Wi\approx 80\). The polymers do not alter the large-scale turbulent structure, but hydrodynamic interactions generate…