1,730 research outputs found

### Moderate deviations for the spectral measure of certain random matrices

We derive a moderate deviations principle for matrices of the form XN = DN + WN where WN are Wigner matrices and DN is a sequence of deterministic matrices whose spectral measures converge in a strong sense to a limit Â”D. Our techniques are based on a dynamical approach introduced by Cabanal-Duvillard and Guionnet

### Lifshitz tails for alloy type models in a constant magnetic field

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed
by a random alloy-type potential constructed with single site potentials
decaying at least at a Gaussian speed. We prove that, if the Landau level stays
preserved as a band edge for the perturbed Hamiltonian, at the Landau levels,
the integrated density of states has a Lifshitz behavior of the type
$e^{-\log^2|E-2bq|}$

### Moderate deviations for the determinant of Wigner matrices

We establish a moderate deviations principle (MDP) for the log-determinant
$\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with
either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate
deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE
ensembles as well as for non-symmetric and non-Hermitian Gaussian random
matrices (Ginibre ensembles), respectively.Comment: 20 pages, one missing reference added; Limit Theorems in Probability,
Statistics and Number Theory, Springer Proceedings in Mathematics and
Statistics, 201

### Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

We consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. It is easy to see that the quenched and the
averaged rate functions are not identically equal. When the dimension is at
least four and Sznitman's transience condition (T) is satisfied, we prove that
these rate functions are finite and equal on a closed set whose interior
contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title
of the paper. To appear in Probability Theory and Related Fields

### Asymptotics for the Wiener sausage among Poissonian obstacles

We consider the Wiener sausage among Poissonian obstacles. The obstacle is
called hard if Brownian motion entering the obstacle is immediately killed, and
is called soft if it is killed at certain rate. It is known that Brownian
motion conditioned to survive among obstacles is confined in a ball near its
starting point. We show the weak law of large numbers, large deviation
principle in special cases and the moment asymptotics for the volume of the
corresponding Wiener sausage. One of the consequence of our results is that the
trajectory of Brownian motion almost fills the confinement ball.Comment: 19 pages, Major revision made for publication in J. Stat. Phy

### Force Modulating Dynamic Disorder: Physical Theory of Catch-slip bond Transitions in Receptor-Ligand Forced Dissociation Experiments

Recently experiments showed that some adhesive receptor-ligand complexes
increase their lifetimes when they are stretched by mechanical force, while the
force increase beyond some thresholds their lifetimes decrease. Several
specific chemical kinetic models have been developed to explain the intriguing
transitions from the "catch-bonds" to the "slip-bonds". In this work we suggest
that the counterintuitive forced dissociation of the complexes is a typical
rate process with dynamic disorder. An uniform one-dimension force modulating
Agmon-Hopfield model is used to quantitatively describe the transitions
observed in the single bond P-selctin glycoprotein ligand
1(PSGL-1)$-$P-selectin forced dissociation experiments, which were respectively
carried out on the constant force [Marshall, {\it et al.}, (2003) Nature {\bf
423}, 190-193] and the force steady- or jump-ramp [Evans {\it et al.}, (2004)
Proc. Natl. Acad. Sci. USA {\bf 98}, 11281-11286] modes. Our calculation shows
that the novel catch-slip bond transition arises from a competition of the two
components of external applied force along the dissociation reaction coordinate
and the complex conformational coordinate: the former accelerates the
dissociation by lowering the height of the energy barrier between the bound and
free states (slip), while the later stabilizes the complex by dragging the
system to the higher barrier height (catch).Comment: 8 pages, 3 figures, submitte

### Moderate deviation principle for ergodic Markov chain. Lipschitz summands

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1,$ where
$(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in \mathbb{R}^d$,
when the spectrum of operator $P_x$ is continuous. The vector-valued function
$H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is
required. The main helpful tools in our approach are Poisson's equation and
Stochastic Exponential; the first enables to replace the original family by
$\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to avoid the
direct Laplace transform analysis

### Quenched large deviations for multidimensional random walk in random environment with holding times

We consider a random walk in random environment with random holding times,
that is, the random walk jumping to one of its nearest neighbors with some
transition probability after a random holding time. Both the transition
probabilities and the laws of the holding times are randomly distributed over
the integer lattice. Our main result is a quenched large deviation principle
for the position of the random walk. The rate function is given by the Legendre
transform of the so-called Lyapunov exponents for the Laplace transform of the
first passage time. By using this representation, we derive some asymptotics of
the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page

- âŠ