相关论文: Annealed upper tails for the energy of a polymer
We consider the energy of a randomly charged polymer. We assume that only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we…
We study an undirected polymer chain living on the 1-dimensional integer lattice and carrying i.i.d.\ random charges. Each self-intersection of the polymer contributes to the Hamiltonian an energy that is equal to the product of the charges…
This paper considers an undirected polymer chain on $\mathbb{Z}^d$, $d \geq 2$, with i.i.d.\ random charges attached to its constituent monomers. Each self-intersection of the polymer chain contributes an energy to the interaction…
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
We discuss the quenched tail estimates for the random walk in random scenery. The random walk is the symmetric nearest neighbor walk and the random scenery is assumed to be independent and identically distributed, non-negative, and has a…
In this paper, we consider the linearly reinforced and the once-reinforced random walk models in the transient phase on trees. We show the large deviations for the upper tails for both models. We also show the exponential decay for the…
We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
We study models of continuous time, symmetric, $\Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We…
We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…
We consider a model of a polymer in $\mathbb{Z}^{d+1}$, constrained to join 0 and a hyperplane at distance $N$. The polymer is subject to a quenched nonnegative random environment. Alternatively, the model describes crossing random walks in…
We study the range of a planar random walk on a randomly oriented lattice, already known to be transient. We prove that the expectation of the range grows linearly, in both the quenched (for a.e. orientation) and annealed ("averaged")…
The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances on their synthesis. The self-assembly pathways are typically…
The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions is investigated theoretically. Various statistical charge distributions along the polyelectrolyte chains are considered: smeared, annealed, permuted and quenched.…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
We study Brownian motion in a drifted Brownian potential in the subexponential regime. We prove that the annealed probability of deviating below the almost sure speed has a polynomial rate of decay and compute the exponent in this power…
Monte Carlo simulations are used to study the non-uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under theta-solvent conditions and with added salt. Within a range of the order of the Debye length…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…