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math.PR2026
Trimmed branching random walk and a free obstacle problem
Rami Atar, Leonid Mytnik, Gershon Wolansky
Consider particles performing random walks on the -grid , with branching and density-dependent selection: When one of the particles branches, a particle is rem…
math.PR2025
Heavy traffic limit with discontinuous coefficients via a non-standard semimartingale decomposition
Rami Atar, Masakiyo Miyazawa
This paper studies a single server queue in heavy traffic, with general inter-arrival and service time distributions, where arrival and service rates vary discontinuously as a func…
math.PR2024
Rank-based stochastic differential inclusions and diffusion limits for a load balancing model
Rami Atar, Tomoyuki Ichiba
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream…