arXiv subjects

Ruichao Jiang

Publications and source records attributed to Ruichao Jiang.

11 recordsLinked to original sources

arXiv2026

A contribution to the critique of blockchain censorship

We study the blockchain censorship attack introduced in [21], which shows that joining the attack is a dominant strategy. We show that, by introducing certain detectability threshold, joining the attack can lead to strictly less reward for whales, which are defined to be a small number of validators that hold significantly more voting power than the rest (henceforth known as minnows). This leads to a change of the equilibrium: With whales unwilling to participate in the attack, it is difficult for minnows alone to launch the attack. We also perform Monte Carlo simulation to show the existence of reduction for whales' reward in Ethereum and Solana.

cs.CR↗

arXiv2026

Target Weight Mechanism doesn't make delta hedge easier

Chitra et al. (2025) claim that Target Weight Mechanism (TWM) in Perpetual Demand Lending Pools (PDLPs) can lower the delta of the portfolio under certain condition. We prove that their condition is self-contradictory. Furthermore, we prove an impossibility result that no TWM can lower the delta uniformly.

q-fin.RM↗

arXiv2026

Concave Continuation: Linking Routing to Arbitrage

We extend AMM trade functions to negative inputs via the \textit{concave continuation}, derived from the invariance of the local conservation law under allocation direction flips. This unifies routing and arbitrage into a single problem. We extend the one-hop transfer algorithm proposed in \cite{jiang} to this setting.

math.OC↗

arXiv2026

On the Convergence Rate of the One-Hop Transfer Algorithm

The transfer algorithm~\cite{jiang} solves the on-chain one-hop swap routing problem. In \cite{jiang}, the convergence is proved but the convergence rate is left open. We prove that the algorithm terminates in at most $\mathcal{O}(N\kappa\log\frac{1}{\varepsilon})$ rounds, where $N$ is the number of AMMs, $\kappa$ a liquidity heterogeneity parameter and $\varepsilon$ a tolerance parameter.

math.OC↗

arXiv2025

Chasing price drains liquidity

Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and exponentially fast decay of liquidity. Next, assuming that there is a Centralized Exchange (CEX), in which the price follows a GBM and the AMM price mean reverts to the CEX price, we show numerically that the same strategy still leads to decay. Last, we propose a strategy that increases the liquidity even without compounding fees earned through liquidity provision.

cs.CE↗

arXiv2023

Robbed withdrawal

In this article we show that Theorem 2 in Lie et al. (2023) is incorrect. Since Wombat Exchange, a decentralized exchange, is built upon Lie et al. (2023) and Theorem 2 is fundamental to Wombat Finance, we show that an undesirable phenomenon, which we call the robbed withdrawal, can happen as a consequence.

cs.CR↗

arXiv2022

Hitting time for Markov decision process

We define the hitting time for a Markov decision process (MDP). We do not use the hitting time of the Markov process induced by the MDP because the induced chain may not have a stationary distribution. Even it has a stationary distribution, the stationary distribution may not coincide with the (normalized) occupancy measure of the MDP. We observe a relationship between the MDP and the PageRank. Using this observation, we construct an MP whose stationary distribution coincides with the normalized occupancy measure of the MDP and we define the hitting time of the MDP as the hitting time of the associated MP.

cs.LG↗

arXiv2022

Laplacian operator on statistical manifold

In this paper, we define a Laplacian operator on a statistical manifold, called the vector Laplacian. This vector Laplacian incorporates information from the Amari-Chentsov tensor. We derive a formula for the vector Laplacian. We also give two applications using the heat kernel associated with the vector Laplacian.

math.DG↗

arXiv2020

Information geometry and Frobenius algebra

We show that a Frobenius sturcture is equivalent to a dually flat sturcture in information geometry. We define a multiplication structure on the tangent spaces of statistical manifolds, which we call the statistical product. We also define a scalar quantity, which we call the Yukawa term. By showing two examples from statistical mechanics, first the classical ideal gas, second the quantum bosonic ideal gas, we argue that the Yukawa term quantifies information generation, which resembles how mass is generated via the 3-points interaction of two fermions and a Higgs boson (Higgs mechanism). In the classical case, The Yukawa term is identically zero, whereas in the quantum case, the Yukawa term diverges as the fugacity goes to zero, which indicates the Bose-Einstein condensation.

math.DG↗

arXiv2020

An upper bound and criteria for the Galois group of weighted walks with rational coefficients in the quarter plane

Using Mazur's theorem on torsions of elliptic curves, an upper bound 24 for the order of the finite Galois group $\mathcal{H}$ associated with weighted walks in the quarter plane $\mathbb{Z}^2_+$ is obtained. The explicit criterion for $\mathcal{H}$ to have order 4 or 6 is rederived by simple geometric argument. Using division polynomials, a recursive criterion for $\mathcal{H}$ having order $4m$ or $4m+2$ is also obtained. As a corollary, explicit criterion for $\mathcal{H}$ to have order 8 is given and is much simpler than the existing method.

math.NT↗

arXiv2020

Weyl Prior and Bayesian Statistics

When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the $α$-parallel prior,, which generalized the Jeffreys prior by exploiting higher-order geometric object, known as Chentsov-Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the $α$-parallel prior with the parameter $α$ equals $-n$, where $n$ is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of $α$-connections. This makes the choice for the parameter $α$ more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.

math.DG↗