775 research outputs found
Diffusion Limited Aggregation on a Cylinder
We consider the DLA process on a cylinder G x N. It is shown that this
process "grows arms", provided that the base graph G has small enough mixing
time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the
time it takes the cluster to reach the m-th layer of the cylinder is at most of
order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs
of degree 5, for which the DLA cluster on these graphs has arbitrarily small
density.
In addition, we provide an upper bound on the rate at which the "arms" grow.
This bound is valid for a large class of base graphs G, including discrete tori
of dimension at least 3.
It is also shown that for any base graph G, the density of the DLA process on
a G-cylinder is related to the rate at which the arms of the cluster grow. This
implies, that for any vertex transitive G, the density of DLA on a G-cylinder
is bounded by 2/3.Comment: 1 figur
A derivative formula for the free energy function
We consider bond percolation on the lattice. Let be the
number of open clusters in . It is well known that converges to the free energy function at the zero field.
In this paper, we show that converges to
.Comment: 8 pages 1 figur
Transient Random Walks in Random Environment on a Galton-Watson Tree
We consider a transient random walk in random environment on a
Galton--Watson tree. Under fairly general assumptions, we give a sharp and
explicit criterion for the asymptotic speed to be positive. As a consequence,
situations with zero speed are revealed to occur. In such cases, we prove that
is of order of magnitude , with . We also
show that the linearly edge reinforced random walk on a regular tree always has
a positive asymptotic speed, which improves a recent result of Collevecchio
\cite{Col06}
Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems
The model checking problem for propositional dynamic logic (PDL) over message
sequence charts (MSCs) and communicating finite state machines (CFMs) asks,
given a channel bound , a PDL formula and a CFM ,
whether every existentially -bounded MSC accepted by
satisfies . Recently, it was shown that this problem is
PSPACE-complete.
In the present work, we consider CRPDL over MSCs which is PDL equipped with
the operators converse and repeat. The former enables one to walk back and
forth within an MSC using a single path expression whereas the latter allows to
express that a path expression can be repeated infinitely often. To solve the
model checking problem for this logic, we define message sequence chart
automata (MSCAs) which are multi-way alternating parity automata walking on
MSCs. By exploiting a new concept called concatenation states, we are able to
inductively construct, for every CRPDL formula , an MSCA precisely
accepting the set of models of . As a result, we obtain that the model
checking problem for CRPDL and CFMs is still in PSPACE
First passage time distribution for a random walker on a random forcing energy landscape
We present an analytical approximation scheme for the first passage time
distribution on a finite interval of a random walker on a random forcing energy
landscape. The approximation scheme captures the behavior of the distribution
over all timescales in the problem. The results are carefully checked against
numerical simulations.Comment: 16 page
Enhancing Approximations for Regular Reachability Analysis
This paper introduces two mechanisms for computing over-approximations of
sets of reachable states, with the aim of ensuring termination of state-space
exploration. The first mechanism consists in over-approximating the automata
representing reachable sets by merging some of their states with respect to
simple syntactic criteria, or a combination of such criteria. The second
approximation mechanism consists in manipulating an auxiliary automaton when
applying a transducer representing the transition relation to an automaton
encoding the initial states. In addition, for the second mechanism we propose a
new approach to refine the approximations depending on a property of interest.
The proposals are evaluated on examples of mutual exclusion protocols
Alternative proof for the localization of Sinai's walk
We give an alternative proof of the localization of Sinai's random walk in
random environment under weaker hypothesis than the ones used by Sinai.
Moreover we give estimates that are stronger than the one of Sinai on the
localization neighborhood and on the probability for the random walk to stay
inside this neighborhood
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School Choice with Consent: An Experiment
Public school choice often yields student assignments that are neither fair nor efficient. The efficiency-adjusted deferred acceptance mechanism (EADAM) allows students to consent to waive priorities that have no effect on their assignments. A burgeoning recent literature places EADAM at the centre of the trade-off between efficiency and fairness in school choice. Meanwhile, the Flemish Ministry of Education has taken the first steps to implement this algorithm in Belgium. We provide the first experimental evidence on the performance of EADAM against the celebrated deferred acceptance mechanism (DA). We find that both efficiency and truth-telling rates are higher under EADAM than under DA, even though EADAM is not strategy-proof. When the priority waiver is enforced, efficiency further increases, while truth-telling rates decrease relative to the EADAM variants where students can dodge the waiver. Our results challenge the importance of strategy-proofness as a prerequisite for truth-telling and portend a new trade-off between efficiency and vulnerability to preference manipulation
Parallelizing Synthesis from Temporal Logic Specifications by Identifying Equicontrollable States
For the synthesis of correct-by-construction control policies from temporal logic specifications the scalability of the synthesis algorithms is often a bottleneck. In this paper, we parallelize synthesis from specifications in the GR(1) fragment of linear temporal logic by introducing a hierarchical procedure that allows decoupling of the fixpoint computations. The state space is partitioned into equicontrollable sets using solutions to parametrized games that arise from decomposing the original GR(1) game into smaller reachability-persistence games. Following the partitioning, another synthesis problem is formulated for composing the strategies from the decomposed reachability games. The formulation guarantees that composing the synthesized controllers ensures satisfaction of the given GR(1) property. Experiments with robot planning problems demonstrate good performance of the approach
The partially asymmetric zero range process with quenched disorder
We consider the one-dimensional partially asymmetric zero range process where
the hopping rates as well as the easy direction of hopping are random
variables. For this type of disorder there is a condensation phenomena in the
thermodynamic limit: the particles typically occupy one single site and the
fraction of particles outside the condensate is vanishing. We use extreme value
statistics and an asymptotically exact strong disorder renormalization group
method to explore the properties of the steady state. In a finite system of
sites the current vanishes as , where the dynamical exponent,
, is exactly calculated. For the transport is realized by active particles, which move with a constant velocity, whereas for
the transport is due to the anomalous diffusion of a single Brownian
particle. Inactive particles are localized at a second special site and their
number in rare realizations is macroscopic. The average density profile of
inactive particles has a width of, , in terms of the
asymmetry parameter, . In addition to this, we have investigated the
approach to the steady state of the system through a coarsening process and
found that the size of the condensate grows as for large
times. For the unbiased model is formally infinite and the coarsening is
logarithmically slow.Comment: 12 pages, 9 figure
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