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On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became...
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Obstacle Problems with Double Boundary Condition for Least Gradient Functions in Metric Measure Spaces
In the setting of a metric space equipped with a doubling measure supporting a (1, 1)-Poincaré inequality, we study the problem of minimizing the...
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Free boundary dimers: random walk representation and scaling limit
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly...
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Anomalous diffusion limit for a kinetic equation with a thermostatted interface
We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the...
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Lie Symmetries Methods in Boundary Crossing Problems for Diffusion Processes
This paper uses Lie symmetry methods to analyze boundary crossing probabilities for a large class of diffusion processes. We show that if the...
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A formula for boundary correlations of the critical Ising model
Given a finite rhombus tiling of a polygonal region in the plane, the associated critical Z -invariant Ising model is invariant under star-triangle...
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Short Topological Decompositions of Non-orientable Surfaces
In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result...
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Exit Versus Escape for Stochastic Dynamical Systems and Application to the Computation of the Bursting Time Duration in Neuronal Networks
We study the exit time of two-dimensional dynamical systems perturbed by a small noise that exhibits two peculiar behaviors: (1) The maximum of the...
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Some Boundary Harnack Principles with Uniform Constants
We prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.
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Random colorings in manifolds
We develop a general method for constructing random manifolds and sub-manifolds in arbitrary dimensions. The method is based on associating colors to...
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On Extension of the Markov Chain Approximation Method for Computing Feynman–Kac Type Expectations
An efficient discrete time and space Markov chain approximation employing a Brownian bridge correction for computing curvilinear boundary crossing...
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Conformal Restriction Measures on Loops Surrounding an Interior Point
A conformal restriction measure is a probability measure which is used to describe the law of a random connected subset in a simply connected domain...
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A Smaller Upper Bound for the \((4,8^2)\) Lattice Site Percolation Threshold
The \((4,8^2)\) , or “bathroom tile,” lattice is one of the...
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Quantitative Russo–Seymour–Welsh for Random Walk on Random Graphs and Decorrelation of Uniform Spanning Trees
We prove a quantitative Russo–Seymour–Welsh (RSW)-type result for random walks on two natural examples of random planar graphs: the supercritical...
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