1,007 research outputs found
Almost sure estimates for the concentration neighborhood of Sinai's walk
We consider Sinai's random walk in random environment. We prove that
infinitely often (i.o.) the size of the concentration neighborhood of this
random walk is almost surely bounded. As an application we get that i.o. the
maximal distance between two favorite sites is almost surely bounded
The local time of a random walk on growing hypercubes
We study a random walk in a random environment (RWRE) on , . The main assumptions are that conditionned on the environment the
random walk is reversible. Moreover we construct our environment in such a way
that the walk can't be trapped on a single point like in some particular RWRE
but in some specific d-1 surfaces. These surfaces are basic surfaces with
deterministic geometry. We prove that the local time in the neighborhood of
these surfaces is driven by a function of the (random) reversible measure. As
an application we get the limit law of the local time as a process on these
surfaces.Comment: 24 page
Time Travel and the Immutability of the Past within B-Theoretical Models
The goal of this paper is to defend the general tenet that time travelers cannot change the past within B-theoretical models of time, independently of how many temporal dimensions there are. Baron Pacific Philosophical Quarterly, 98, 129–147 offered a strong argument intended to reach this general conclusion. However, his argument does not cover a peculiar case, i.e. a B-theoretical one-dimensional model of time that allows for the presence of internal times. Loss Pacific Philosophical Quarterly, 96, 1–11 used the latter model to argue that time travelers can change the past within such model. We show a way to debunk Loss’s argument, so that the general tenet about the impossibility of changing the past within B-theoretical models is maintained
Limit law of the local time for Brox's diffusion
We consider Brox's model: a one-dimensional diffusion in a Brownian potential
W. We show that the normalized local time process (L(t;m_(log t) + x)=t; x \in
R), where m_(log t) is the bottom of the deepest valley reached by the process
before time t, behaves asymptotically like a process which only depends on W.
As a consequence, we get the weak convergence of the local time to a functional
of two independent three-dimensional Bessel processes and thus the limit law of
the supremum of the normalized local time. These results are discussed and
compared to the discrete time and space case which same questions have been
solved recently by N. Gantert, Y. Peres and Z. Shi
Renewal structure and local time for diffusions in random environment
We study a one-dimensional diffusion in a drifted Brownian potential
, with 0\textless{}\kappa\textless{}1, and focus on the behavior
of the local times of before time
t\textgreater{}0.In particular we characterize the limit law of the supremum
of the local time, as well as the position of the favorite sites. These limits
can be written explicitly from a two dimensional stable L{\'e}vy process. Our
analysis is based on the study of an extension of the renewal structure which
is deeply involved in the asymptotic behavior of .Comment: 61 page
A limit result for a system of particles in random environment
We consider an infinite system of particles in one dimension, each particle
performs independant Sinai's random walk in random environment. Considering an
instant , large enough, we prove a result in probability showing that the
particles are trapped in the neighborhood of well defined points of the lattice
depending on the random environment the time and the starting point of the
particles.Comment: 11 page
Back to the (Branching) Future
The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branching-tree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show that there is an incompatibility between the way branching-tree models account for the open future and the possibility of time travel. That is, I argue that once time travel enters the picture, branching time fails to model the openness of the future by means of alternative future branches. I show how this holds independently of whether branching-time models are cashed out in A-theoretic or B-theoretic terms
On the concentration of Sinai's walk
We consider Sinai's random walk in random environment. We prove that for an interval of time [1,n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi totality of this amount of time. Moreover the local time at the point of localization normalized by converges in probability to a well defined random variable of the environment
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