548 research outputs found
Boundary crossing Random Walks, clinical trials and multinomial sequential estimation
A sufficient condition for the uniqueness of multinomial sequential unbiased
estimators is provided generalizing a classical result for binomial samples.
Unbiased estimators are applied to infer the parameters of multidimensional or
multinomial Random Walks which are observed until they reach a boundary. An
application to clinical trials is presented
Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
We propose a reaction-transport model for CTRW with non-linear reactions and
non-exponential waiting time distributions. We derive non-linear evolution
equation for mesoscopic density of particles. We apply this equation to the
problem of fronts propagation into unstable state of reaction-transport systems
with anomalous diffusion. We have found an explicit expression for the speed of
propagating front in the case of subdiffusion transport.Comment: 7 page
Coagulation by Random Velocity Fields as a Kramers Problem
We analyse the motion of a system of particles suspended in a fluid which has
a random velocity field. There are coagulating and non-coagulating phases. We
show that the phase transition is related to a Kramers problem, and use this to
determine the phase diagram, as a function of the dimensionless inertia of the
particles, epsilon, and a measure of the relative intensities of potential and
solenoidal components of the velocity field, Gamma. We find that the phase line
is described by a function which is non-analytic at epsilon=0, and which is
related to escape over a barrier in the Kramers problem. We discuss the
physical realisations of this phase transition.Comment: 4 pages, 3 figure
Convergence of resonances on thin branched quantum wave guides
We prove an abstract criterion stating resolvent convergence in the case of
operators acting in different Hilbert spaces. This result is then applied to
the case of Laplacians on a family X_\eps of branched quantum waveguides.
Combining it with an exterior complex scaling we show, in particular, that the
resonances on X_\eps approximate those of the Laplacian with ``free''
boundary conditions on , the skeleton graph of X_\eps.Comment: 48 pages, 1 figur
On population extinction risk in the aftermath of a catastrophic event
We investigate how a catastrophic event (modeled as a temporary fall of the
reproduction rate) increases the extinction probability of an isolated
self-regulated stochastic population. Using a variant of the Verhulst logistic
model as an example, we combine the probability generating function technique
with an eikonal approximation to evaluate the exponentially large increase in
the extinction probability caused by the catastrophe. This quantity is given by
the eikonal action computed over "the optimal path" (instanton) of an effective
classical Hamiltonian system with a time-dependent Hamiltonian. For a general
catastrophe the eikonal equations can be solved numerically. For simple models
of catastrophic events analytic solutions can be obtained. One such solution
becomes quite simple close to the bifurcation point of the Verhulst model. The
eikonal results for the increase in the extinction probability caused by a
catastrophe agree well with numerical solutions of the master equation.Comment: 11 pages, 11 figure
Statistical mechanics of spatial evolutionary games
We discuss the long-run behavior of stochastic dynamics of many interacting
players in spatial evolutionary games. In particular, we investigate the effect
of the number of players and the noise level on the stochastic stability of
Nash equilibria. We discuss similarities and differences between systems of
interacting players maximizing their individual payoffs and particles
minimizing their interaction energy. We use concepts and techniques of
statistical mechanics to study game-theoretic models. In order to obtain
results in the case of the so-called potential games, we analyze the
thermodynamic limit of the appropriate models of interacting particles.Comment: 19 pages, to appear in J. Phys.
Heat bounds and the blowtorch theorem
We study driven systems with possible population inversion and we give
optimal bounds on the relative occupations in terms of released heat. A precise
meaning to Landauer's blowtorch theorem (1975) is obtained stating that
nonequilibrium occupations are essentially modified by kinetic effects. Towards
very low temperatures we apply a Freidlin-Wentzel type analysis for continuous
time Markov jump processes. It leads to a definition of dominant states in
terms of both heat and escape rates.Comment: 11 pages; v2: minor changes, 1 reference adde
Scattering solutions in a network of thin fibers: small diameter asymptotics
Small diameter asymptotics is obtained for scattering solutions in a network
of thin fibers. The asymptotics is expressed in terms of solutions of related
problems on the limiting quantum graph. We calculate the Lagrangian gluing
conditions at vertices for the problems on the limiting graph. If the frequency
of the incident wave is above the bottom of the absolutely continuous spectrum,
the gluing conditions are formulated in terms of the scattering data for each
individual junction of the network
Path integral approach to random motion with nonlinear friction
Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.Comment: 18 pages, 3 figure
Large Deviation Analysis of Rapid Onset of Rain Showers
Rainfall from ice-free cumulus clouds requires collisions of large numbers of microscopic droplets to create every raindrop. The onset of rain showers can be surprisingly rapid, much faster than the mean time required for a single collision. Large-deviation theory is used to explain this observation
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