The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficien... more The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficient in Byzantine infrastructure. We propose an adaption of the FPC to a setting where the voting power is proportional to the nodes reputations. We model the reputation using a Zipf law and show using simulations that the performance of the protocol in Byzantine infrastructure increases with the Zipf exponent. Moreover, we propose several improvements of the FPC that decrease the failure rates significantly and allow the protocol to withstand adversaries with higher weight. We distinguish between cautious and berserk strategies of the adversaries and propose an efficient method to detect the more harmful berserk strategies. Our study refers at several points to a specific implementation of the IOTA protocol, but the principal results hold for general implementations of reputation models.
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Rényi strong law for the increments.
We base ourselves on the construction of the two-dimensional random interlacements [12] to define... more We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin, which makes them transient. We also compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements' local time for sites far from the origin and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements' local times.
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Rényi– Shepp strong law for the increments. 1. Definitions and main results The classical Erdős-Rényi–Shepp strong law of large numbers [4], [5], asserts as follows. Theorem 1.1 (Erdős-Rényi 1970, Shepp 1964). Consider a random walk Sn = ∑n i=1Xi with Xi i.i.d., satisfying EX1 = 0. Set φ(t) = E[e tX ] and let D φ = {t > 0 : φ(t) < ∞}. Let α > 0 be such that φ(t)e −αt achieves its minimum value for some t in the interior of D φ . Set 1/Aα := − logmin t>0 φ(t)e −αt. Then, Aα > 0 and (1.1) max 0≤j≤n−⌊Aα logn⌋ Sj+⌊Aα logn⌋ − Sj ⌊Aα log n⌋ a.s. → α, a.s. In the particular case of Xi ∈ {−1, 1}, the assumptions of the theorem are satisfied for any α ∈ (0, 1). The theorem also trivially generalizes to EX1 ̸= 0, by considering Yi = Xi − EXi. Theorem 1.1 is closely related to the large deviation principle for Sn/n given by Cramér’s theorem, see e.g. [3] for background...
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Renyi strong law for the increments.
The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficien... more The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficient in Byzantine infrastructure. We propose an adaption of the FPC to a setting where the voting power is proportional to the nodes reputations. We model the reputation using a Zipf law and show using simulations that the performance of the protocol in Byzantine infrastructure increases with the Zipf exponent. Moreover, we propose several improvements of the FPC that decrease the failure rates significantly and allow the protocol to withstand adversaries with higher weight. We distinguish between cautious and berserk strategies of the adversaries and propose an efficient method to detect the more harmful berserk strategies. Our study refers at several points to a specific implementation of the IOTA protocol, but the principal results hold for general implementations of reputation models.
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Rényi strong law for the increments.
We base ourselves on the construction of the two-dimensional random interlacements [12] to define... more We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin, which makes them transient. We also compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements' local time for sites far from the origin and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements' local times.
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Rényi– Shepp strong law for the increments. 1. Definitions and main results The classical Erdős-Rényi–Shepp strong law of large numbers [4], [5], asserts as follows. Theorem 1.1 (Erdős-Rényi 1970, Shepp 1964). Consider a random walk Sn = ∑n i=1Xi with Xi i.i.d., satisfying EX1 = 0. Set φ(t) = E[e tX ] and let D φ = {t > 0 : φ(t) < ∞}. Let α > 0 be such that φ(t)e −αt achieves its minimum value for some t in the interior of D φ . Set 1/Aα := − logmin t>0 φ(t)e −αt. Then, Aα > 0 and (1.1) max 0≤j≤n−⌊Aα logn⌋ Sj+⌊Aα logn⌋ − Sj ⌊Aα log n⌋ a.s. → α, a.s. In the particular case of Xi ∈ {−1, 1}, the assumptions of the theorem are satisfied for any α ∈ (0, 1). The theorem also trivially generalizes to EX1 ̸= 0, by considering Yi = Xi − EXi. Theorem 1.1 is closely related to the large deviation principle for Sn/n given by Cramér’s theorem, see e.g. [3] for background...
We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We ... more We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erdős-Renyi strong law for the increments.
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Papers by Darcy Camargo