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Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Learning Decision-Sufficient Representations for Linear Optimization Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses Prabhakar function and unified fractional kinetic equation in bicomplex space Computing Gamma(p/q) with Beta function values Flows on Graded Manifolds Optimal embedding dimension in the Nash--Tognoli theorem An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit Sharp Bohr-Type inequalities for certain classes of close-to-convex functions Invariants of real affine varieties based on their complexifications Topological symmetric and braid homologies A Formal Graph-Theoretic Framework for Pitch Class Set Analysis Finite groups with high commuting probability for Sylow subgroups Performance Bounds for Rollout Policies in Stochastic Shortest Path Problems Real 2-blocks in quasi-simple groups Maximal subalgebras of the Lie algebra $W_n(\mathbb{K})$ Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$ Global analysis of the Kuramoto flow Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? 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Maximum occupation time of a transient excited random walk on Z
Reza Rastegar, Alexander Roitershtein · 2011-11-05 · via math updates on arXiv.org

We consider a transient excited random walk on $Z$ and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that, in contrast to the random walks in random environment, a transient excited random walk does not spend an asymptotically positive fraction of time at its favorite (most visited up to a date) sites.

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