A lower bound on the growth exponent for loop-erased random walk in two dimensions
A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
The growth exponent α for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius n is of order nα. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.
A mathematical model of an In Vitro experiment to investigate endothelial cell migration.
A matrix with an application to the motion of an absorbing Markov chain. I.
A model and application of binary random sequence with probabilities depending on history
This paper presents a model of binary random sequence with probabilities depending on previous sequence values as well as on a set of covariates. Both these dependencies are expressed via the logistic regression model, such a choice enables an easy and reliable model parameters estimation. Further, a model with time-depending parameters is considered and method of solution proposed. The main objective is then the application dealing with both artificial and real data cases, illustrating the method...
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