Related papers: Sideways on the highways
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire…
This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…
Navigation through narrow passages during colony relocation by the tandem-running ants, $\textit{Diacamma}$ $\textit{indicum}$, is a tour de force of biological traffic coordination. Even on one-lane paths, the ants tactfully manage a…
The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the…
Anthropic reasoning is a form of statistical reasoning based upon finding oneself a member of a particular reference class of conscious beings. By considering empirical distribution functions defined over animal life on Earth, we can deduce…
Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
We generalize some results in Hodge theory to generalized normal crossing varieties.
Ants are known to be able to find paths of minimal length between the nest and food sources. The deposit of pheromones while they search for food and their chemotactical response to them has been proposed as a crucial element in the…
We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional…
We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be…
Enormous progress have been made in the last 20 years since the publication of our review \cite{csk05polrev} in this journal on transport and traffic phenomena in biology. In this brief article we present a glimpse of the major advances…
We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive…
This is a continuation of our earlier work [Stochastic Processes and their Applications, 129(1), pp.102--128, 2019] on the random walk in random scenery and in random layered conductance. We complete the picture of upper deviation of the…
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…
We study the asymptotic behavior of the simple random walk on oriented version of $\mathbb{Z}^2$. The considered latticesare not directed on the vertical axis but unidirectional on the horizontal one, with symmetric random orientations…
A celebrated result in bifurcation theory is that global connected sets of non-trivial solutions bifurcate from trivial solutions at non-zero eigenvalues of odd algebraic multiplicity of the linearized problem when the operators involved…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…