Distribution of the cumulative sum of a Gaussian distribution

Question

I obtain a random time series by computing the cumulative sum of numbers obtained from a Gaussian distribution:

def gbm():

dti = pd.date_range(start="2018-01-01 17:00", end="2021-01-01 16:00", tz="America/Chicago", freq="T")
gaussian_nums = np.random.normal(0, 1, len(dti))

df = pd.DataFrame(index=dti, columns=["price"])
df["price"] = gaussian_nums
df = df.between_time("17:00", "16:00")

df["price"] = df["price"].cumsum()
df["price"] = df["price"] - df["price"].min()

return df

For reference, the graph of the time series looks like the following:

I was wondering why the distribution of the above time series looks like this:

Is this a known distribution? How do I obtain the pdf?